TY  - JOUR
A1  - Wismath, Shelly
A1  - Koppitz, Jörg
A1  - Denecke, Klaus-Dieter
T1  - Maps between M-solid varieties of emigroups
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Tinpun, Kittisak
A1  - Koppitz, Jörg
T1  - Generating sets of infinite full transformation semigroups with restricted range
JF  - Acta scientiarum mathematicarum
N2  - In the present paper, we consider minimal generating sets of infinite full transformation semigroups with restricted range modulo specific subsets. In particular, we determine relative ranks.
KW  - generating sets
KW  - transformation semigroups
KW  - restricted range
KW  - relative ranks
Y1  - 2016
U6  - https://doi.org/10.14232/actasm-015-502-4
SN  - 0001-6969
VL  - 82
SP  - 55
EP  - 63
PB  - Institutum Bolyaianum Universitatis Szegediensis
CY  - Szeged
ER  - 
TY  - JOUR
A1  - Shtrakov, Slavcho
A1  - Koppitz, Jörg
T1  - Stable varieties of semigroups and groupoids
JF  - Algebra universalis
N2  - The paper deals with Sigma-composition and Sigma-essential composition of terms which lead to stable and s-stable varieties of algebras. A full description of all stable varieties of semigroups, commutative and idempotent groupoids is obtained. We use an abstract reduction system which simplifies the presentations of terms of type tau - (2) to study the variety of idempotent groupoids and s-stable varieties of groupoids. S-stable varieties are a variation of stable varieties, used to highlight replacement of subterms of a term in a deductive system instead of the usual replacement of variables by terms.
KW  - composition of terms
KW  - essential position in terms
KW  - stable variety
Y1  - 2016
U6  - https://doi.org/10.1007/s00012-015-0359-7
SN  - 0002-5240
SN  - 1420-8911
VL  - 75
SP  - 85
EP  - 106
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Musunthia, Tiwadee
A1  - Koppitz, Jörg
T1  - Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set
JF  - Forum mathematicum
N2  - In this paper, we study the maximal subsemigroups of several semigroups of order-preserving transformations on the natural numbers and the integers, respectively. We determine all maximal subsemigroups of the monoid of all order-preserving injections on the set of natural numbers as well as on the set of integers. Further, we give all maximal subsemigroups of the monoid of all bijections on the integers. For the monoid of all order-preserving transformations on the natural numbers, we classify also all its maximal subsemigroups, containing a particular set of transformations.
KW  - Transformation semigroups
KW  - maximal subsemigroups
KW  - order-preserving mappings
Y1  - 2017
U6  - https://doi.org/10.1515/forum-2015-0093
SN  - 0933-7741
SN  - 1435-5337
VL  - 29
SP  - 971
EP  - 984
PB  - De Gruyter
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Koppitz, Jörg
A1  - Supaporn, Worakrit
T1  - Categary equivalences of clones of operations preserving unaryoperations
JF  - COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
N2  - Any clones on arbitrary set A can be written of the form Pol (A)Q for some set Q of relations on A. We consider clones of the form Pal (A)Q where Q is a set of unary relations on a finite set A. A clone Pol (A)Q is said to be a clone on a set of the smallest cardinality with respect to category equivalence if vertical bar A vertical bar <= vertical bar S vertical bar for all finite sets S and all clones C on S that category equivalent to Pol (A)Q. We characterize the clones on a set of the smallest cardinality with respect to category equivalent and show how we can find a clone on a set of the smallest cardinality that category equivalent to a given clone.
KW  - category equivalence of clones
KW  - clone of operations
Y1  - 2013
SN  - 1310-1331
VL  - 66
IS  - 2
SP  - 177
EP  - 184
PB  - Publ. House of the Bulgarian Acad. of Sciences
CY  - Sofia
ER  - 
TY  - JOUR
A1  - Koppitz, Jörg
A1  - Musunthia, Tiwadee
T1  - Maximal subsemigroups containing a particular semigroup
JF  - Mathematica Slovaca
N2  - We characterize maximal subsemigroups of the monoid T(X) of all transformations on the set X = a"center dot of natural numbers containing a given subsemigroup W of T(X) such that T(X) is finitely generated over W. This paper gives a contribution to the characterization of maximal subsemigroups on the monoid of all transformations on an infinite set.
KW  - maximal subsemigroup
KW  - transformations on infinite set
Y1  - 2014
U6  - https://doi.org/10.2478/s12175-014-0280-0
SN  - 0139-9918
SN  - 1337-2211
VL  - 64
IS  - 6
SP  - 1369
EP  - 1380
PB  - De Gruyter
CY  - Warsaw
ER  - 
TY  - INPR
A1  - Koppitz, Jörg
A1  - Musunthia, Tiwadee
T1  - Maximal subsemigroups containing a particular semigroup
N2  - We study maximal subsemigroups of the monoid T(X) of all full transformations on the set X = N of natural numbers containing a given subsemigroup W of T(X), where each element of a given set U is a generator of T(X) modulo W. This note continues the study of maximal subsemigroups of the monoid of all full transformations on an infinite set.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 8 
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57465
ER  - 
TY  - JOUR
A1  - Koppitz, Jörg
T1  - M-solid subvarieties of some varieties of commutative semigroups
Y1  - 1997
ER  - 
TY  - THES
A1  - Koppitz, Jörg
T1  - Über Halbgruppen mit vereinigungshalbdistributivem Unterhalbgruppenverband
Y1  - 1993
ER  - 
TY  - JOUR
A1  - Koppitz, Jörg
T1  - All Reg-solid varieties of commutative semigroups
N2  - We determine all regular solid varieties of commutative semigroups. Each of them is contained in the Reg- hyperequational class V (RC) defined by the associative law and the commutative law, and every subvariety of V (RC) is regular solid. In the present paper, the subvariety lattice of V (RC) will be characterized.
Y1  - 2009
UR  - http://www.springerlink.com/content/103374
U6  - https://doi.org/10.1007/s00233-008-9124-y
SN  - 0037-1912
ER  - 
TY  - JOUR
A1  - Koppitz, Jörg
T1  - Separation of O-n from its proper subsemigroups by a single identity
JF  - Semigroup forum
N2  - For each , we construct an identity that fails in the semigroup of all order-preserving maps on the -element chain but holds in each proper subsemigroup of O-n.
KW  - Order-preserving maps
KW  - Identities
Y1  - 2015
U6  - https://doi.org/10.1007/s00233-014-9674-0
SN  - 0037-1912
SN  - 1432-2137
VL  - 91
IS  - 1
SP  - 128
EP  - 138
PB  - Springer
CY  - New York
ER  - 
TY  - THES
A1  - Koppitz, Jörg
T1  - M-solide Varietäten von Halbgruppen
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Koppitz, Jörg
T1  - All 2-solid varieties of semigroups
Y1  - 2000
ER  - 
TY  - GEN
A1  - Karpuz, Eylem Guzel
A1  - Çevik, Ahmet Sinan
A1  - Koppitz, Jörg
A1  - Cangul, Ismail Naci
T1  - Some fixed-point results on (generalized) Bruck-Reilly ∗-extensions of monoids
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper, we determine necessary and sufficient conditions for Bruck-Reilly and generalized Bruck-Reilly ∗-extensions of arbitrary monoids to be regular, coregular and strongly π-inverse. These semigroup classes have applications in various field of mathematics, such as matrix theory, discrete mathematics and p-adic analysis (especially in operator theory). In addition, while regularity and coregularity have so many applications in the meaning of boundaries (again in operator theory), inverse monoids and Bruck-Reilly extensions contain a mixture fixed-point results of algebra, topology and geometry within the purposes of this journal.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 942 
KW  - Bruck-Reilly extension
KW  - generalized Bruck-Reilly ∗-extension
KW  - π -inverse monoid
KW  - regular monoid
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-432701
SN  - 1866-8372
IS  - 942
ER  - 
TY  - JOUR
A1  - Karpuz, Eylem Guzel
A1  - Cevik, Ahmet Sinan
A1  - Koppitz, Jörg
A1  - Cangul, Ismail Naci
T1  - Some fixed-point results on (generalized) Bruck-Reilly *-extensions of monoids
JF  - Fixed point theory and applications
N2  - In this paper, we determine necessary and sufficient conditions for Bruck-Reilly and generalized Bruck-Reilly *-extensions of arbitrary monoids to be regular, coregular and strongly pi-inverse. These semigroup classes have applications in various field of mathematics, such as matrix theory, discrete mathematics and p-adic analysis (especially in operator theory). In addition, while regularity and coregularity have so many applications in the meaning of boundaries (again in operator theory), inverse monoids and Bruck-Reilly extensions contain a mixture fixed-point results of algebra, topology and geometry within the purposes of this journal.
KW  - Bruck-Reilly extension
KW  - generalized Bruck-Reilly *-extension
KW  - pi-inverse monoid
KW  - regular monoid
Y1  - 2013
U6  - https://doi.org/10.1186/1687-1812-2013-78
SN  - 1687-1812
IS  - 3
PB  - Springer
CY  - Cham
ER  - 
TY  - JOUR
A1  - Fernandes, Vitor H.
A1  - Koppitz, Jörg
A1  - Musunthia, Tiwadee
T1  - The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence
JF  - Bulletin of the Malaysian Mathematical Sciences Society volume
N2  - A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.
KW  - Transformation semigroups
KW  - Rank of semigroup
KW  - Idempotents
KW  - Order-preserving
KW  - Fence
KW  - Zig-zag order
Y1  - 2019
U6  - https://doi.org/10.1007/s40840-017-0598-1
SN  - 0126-6705
SN  - 2180-4206
VL  - 42
IS  - 5
SP  - 2191
EP  - 2211
PB  - Malaysian mathematical sciences sciences soc
CY  - Pulau Punang
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On the semigroup of all partial fence-preserving injections on a finite set
JF  - Journal of Algebra and Its Applications
N2  - For n∈N , let Xn={a1,a2,…,an} be an n-element set and let F=(Xn;<f) be a fence, also called a zigzag poset. As usual, we denote by In the symmetric inverse semigroup on Xn. We say that a transformation α∈In is fence-preserving if x<fy implies that xα<fyα, for all x,y in the domain of α. In this paper, we study the semigroup PFIn of all partial fence-preserving injections of Xn and its subsemigroup IFn={α∈PFIn:α−1∈PFIn}. Clearly, IFn is an inverse semigroup and contains all regular elements of PFIn. We characterize the Green’s relations for the semigroup IFn. Further, we prove that the semigroup IFn is generated by its elements with rank ≥n−2. Moreover, for n∈2N, we find the least generating set and calculate the rank of IFn.
KW  - Finite transformation semigroup
KW  - fence-preserving transformations
KW  - inverse semigroup
KW  - Green´s Relations
KW  - generators
KW  - rank
Y1  - 2017
U6  - https://doi.org/10.1142/S0219498817502231
SN  - 0219-4988
SN  - 1793-6829
VL  - 16
IS  - 12
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On some anti-inverse transformation semigroups
N2  - A semigroup S is called anti-inverse if for all a E S there is a b is an element of S such that aba = b and bab = a. Each anti-inverse semigroup is regular. In the present paper, we study anti-inverse subsemigroups within the semigroup T-n of all transformations on an n-element set (1 <= n is an element of N). In particular, we characterize all anti-inverse semigroups within the J-classes of T-n and illustrate our result by four examples.
Y1  - 2010
UR  - http://www.proceedings.bas.bg/
SN  - 1310-1331
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On the monoid of all partial order-preserving extensive transformations
JF  - Communications in algebra
N2  - A partial transformation alpha on an n-element chain X-n is called order-preserving if x <= y implies x alpha <= y alpha for all x, y in the domain of alpha and it is called extensive if x <= x alpha for all x in the domain of alpha. The set of all partial order-preserving extensive transformations on X-n forms a semiband POEn. We determine the maximal subsemigroups as well as the maximal subsemibands of POEn.
KW  - Extensive transformation
KW  - Maximal subsemibands
KW  - Maximal subsemigroups
KW  - Rank
KW  - Transformation semigroup
Y1  - 2012
U6  - https://doi.org/10.1080/00927872.2011.557813
SN  - 0092-7872
VL  - 40
IS  - 5
SP  - 1821
EP  - 1826
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations
JF  - Semigroup forum
N2  - We characterize the maximal regular subsemigroups of the ideals of the semigroup of all order-preserving transformations as well as of the semigroup of all order-preserving or order-reversing transformations on a finite ordered set.
KW  - Transformation semigroups
KW  - Regular semigroups
KW  - Order-preserving transformations
KW  - Order-reversing transformations
KW  - Maximal subsemigroups
Y1  - 2011
U6  - https://doi.org/10.1007/s00233-010-9272-8
SN  - 0037-1912
VL  - 82
IS  - 1
SP  - 172
EP  - 180
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range
JF  - Communications in algebra
N2  - Let X be an infinite linearly ordered set and let Y be a nonempty subset of X. We calculate the relative rank of the semigroup OP(X,Y) of all orientation-preserving transformations on X with restricted range Y modulo the semigroup O(X,Y) of all order-preserving transformations on X with restricted range Y. For Y = X, we characterize the relative generating sets of minimal size.
KW  - Order-preserving transformations
KW  - orientation-preserving
KW  - transformations
KW  - relative rank
KW  - restricted range
KW  - transformation
KW  - semigroups on infinite chain
Y1  - 2022
U6  - https://doi.org/10.1080/00927872.2021.2000998
SN  - 0092-7872
SN  - 1532-4125
VL  - 50
IS  - 5
SP  - 2157
EP  - 2168
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On relative ranks of the semigroup of orientation-preserving transformations on infinite chains
JF  - Asian-European journal of mathematics
N2  - In this paper, we determine the relative rank of the semigroup OP(X) of all orientation-preserving transformations on infinite chains modulo the semigroup O(X) of all order-preserving transformations.
KW  - Transformation semigroups on infinite chains
KW  - order-preserving
KW  - transformations
KW  - orientation-preserving transformations
KW  - relative rank
Y1  - 2020
U6  - https://doi.org/10.1142/S1793557121501461
SN  - 1793-5571
SN  - 1793-7183
VL  - 14
IS  - 08
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Fernandes, Vitor H.
A1  - Koppitz, Jörg
T1  - A note on generators of the endomorphism semigroup of an infinite countable chain
JF  - Journal of Algebra and its Applications
N2  - In this note, we consider the semigroup O(X) of all order endomorphisms of an infinite chain X and the subset J of O(X) of all transformations alpha such that vertical bar Im(alpha)vertical bar = vertical bar X vertical bar. For an infinite countable chain X, we give a necessary and sufficient condition on X for O(X) = < J > to hold. We also present a sufficient condition on X for O(X) = < J > to hold, for an arbitrary infinite chain X.
KW  - Infinite chain
KW  - endomorphism semigroup
KW  - generators
KW  - relative rank
Y1  - 2016
U6  - https://doi.org/10.1142/S0219498817500311
SN  - 0219-4988
SN  - 1793-6829
VL  - 16
IS  - 2
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Fernandes, Vitor H.
A1  - Koppitz, Jörg
T1  - The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain
JF  - Publicationes mathematicae
N2  - The study of the semigroups OPn, of all orientation-preserving transformations on an n-element chain, and ORn, of all orientation-preserving or orientation-reversing transformations on an n-element chain, has began in [17] and [5]. In order to bring more insight into the subsemigroup structure of OPn and ORn, we characterize their maximal subsemigroups.
KW  - finite transformation semigroup
KW  - orientation-preserving and orientation-reversing transformations
KW  - maximal subsemigroups
Y1  - 2012
U6  - https://doi.org/10.5486/PMD.2012.4897
SN  - 0033-3883
VL  - 81
IS  - 1-2
SP  - 11
EP  - 29
PB  - Institutum Mathematicum Universitatis Debreceniensis, Debreceni Tudományegyetem Matematikai Intézete
CY  - Debrecen
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
A1  - Štrakov, Slavčo
T1  - Multi-hypersubstitutions and colored solid varieties
JF  - International journal of algebra and computation
N2  - Hypersubstitutions are mappings which map operation symbols to terms. Terms can be visualized by trees. Hypersubstitutions can be extended to mappings defined on sets of trees. The nodes of the trees, describing terms, are labelled by operation symbols and by colors, i.e. certain positive integers. We are interested in mappings which map differently-colored operation symbols to different terms. In this paper we extend the theory of hypersubstitutions and solid varieties to multi-hypersubstitutions and colored solid varieties. We develop the interconnections between such colored terms and multihypersubstitutions and the equational theory of Universal Algebra. The collection of all varieties of a given type forms a complete lattice which is very complex and difficult to study; multi-hypersubstitutions and colored solid varieties offer a new method to study complete sublattices of this lattice.
KW  - coloration of terms
KW  - multi-hypersubstitutions
KW  - colored solid varieties
Y1  - 2006
U6  - https://doi.org/10.1142/S0218196706003189
SN  - 0218-1967
VL  - 16
IS  - 4
SP  - 797
EP  - 815
PB  - World Scient. Publ.
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
A1  - Wismath, Shelly
T1  - The semantical hyperunification problem
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
A1  - Wismath, Shelly
T1  - Solid Varietie of Arbitrary Type
Y1  - 2002
ER  - 
TY  - BOOK
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
A1  - Shtraklov, Slavcho
T1  - The Depth of a Hypersubstitution
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
A1  - Niwczyk, St.
T1  - Equational theories generated by generalized hypersubstitutions of type (n)
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
A1  - Marszalek, R.
T1  - Derived varieties and derived equational theories
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Normal forms of hypersubstitutions
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Finite monoids of hypersubstitutions of type € = (2)
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Pre-solid varieties of commutative semigroups
Y1  - 1995
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - M-solid varieties of semigroups
Y1  - 1995
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Pre-solid varieties of semigroups
Y1  - 1995
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - A characterization of M-solid varieties of semigroups
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - M-solid monoids of hypersubstitutions of type 2
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Hyperassociative semigroups
Y1  - 1994
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Essential variables in weak hypersubstitutions
Y1  - 2000
SN  - 3-8265- 7983-6
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Fluid, unsolid and completely unsolid varieties
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Essential variables in hypersubstitution
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Arworn, Srichan
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Strongly luid and weakly unsolid varieties
Y1  - 2001
SN  - 1346-0862
ER  -