TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg A1 - Wismath, Shelly T1 - The semantical hyperunification problem Y1 - 2001 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 - 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 - Arworn, Srichan A1 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg T1 - Strongly luid and weakly unsolid varieties Y1 - 2001 SN - 1346-0862 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 - 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 - Denecke, Klaus-Dieter A1 - Koppitz, Jörg A1 - Wismath, Shelly T1 - Solid Varietie of Arbitrary Type Y1 - 2002 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 - 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 - Pre-solid varieties of commutative semigroups Y1 - 1995 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;