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; 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 - 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 - 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 - 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 -