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 - JOUR A1 - Koppitz, Jörg T1 - M-solid subvarieties of some varieties of commutative semigroups Y1 - 1997 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 - JOUR A1 - Koppitz, Jörg T1 - All 2-solid varieties of semigroups Y1 - 2000 ER -