TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - A characterization of M-solid varieties of semigroups Y1 - 1999 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 - Koppitz, Jörg T1 - All 2-solid varieties of semigroups Y1 - 2000 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 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 - 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 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 T1 - Essential variables in hypersubstitution Y1 - 2001 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 - Finite monoids of hypersubstitutions of type € = (2) Y1 - 1998 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - Fluid, unsolid and completely unsolid varieties Y1 - 2001 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 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - Hyperassociative semigroups Y1 - 1994 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 - Koppitz, Jörg T1 - M-solid subvarieties of some varieties of commutative semigroups Y1 - 1997 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - M-solid varieties of semigroups Y1 - 1995 ER - TY - THES A1 - Koppitz, Jörg T1 - M-solide Varietäten von Halbgruppen Y1 - 2001 ER - 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 - 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 - 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 - 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 T1 - Normal forms of hypersubstitutions Y1 - 1999 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 - 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 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 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 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;