@article{DimitrovaKoppitz2012, author = {Dimitrova, Ilinka and Koppitz, J{\"o}rg}, title = {On the monoid of all partial order-preserving extensive transformations}, series = {Communications in algebra}, volume = {40}, journal = {Communications in algebra}, number = {5}, publisher = {Taylor \& Francis Group}, address = {Philadelphia}, issn = {0092-7872}, doi = {10.1080/00927872.2011.557813}, pages = {1821 -- 1826}, year = {2012}, abstract = {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.}, language = {en} } @article{DimitrovaFernandesKoppitz2012, author = {Dimitrova, Ilinka and Fernandes, Vitor H. and Koppitz, J{\"o}rg}, title = {The maximal subsemigroups of semigroups of transformations preserving or reversing the orientation on a finite chain}, series = {Publicationes mathematicae}, volume = {81}, journal = {Publicationes mathematicae}, number = {1-2}, publisher = {Institutum Mathematicum Universitatis Debreceniensis, Debreceni Tudom{\´a}nyegyetem Matematikai Int{\´e}zete}, address = {Debrecen}, issn = {0033-3883}, doi = {10.5486/PMD.2012.4897}, pages = {11 -- 29}, year = {2012}, abstract = {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into the subsemigroup structure of OPn and ORn, we characterize their maximal subsemigroups.}, language = {en} } @unpublished{KoppitzMusunthia2012, author = {Koppitz, J{\"o}rg and Musunthia, Tiwadee}, title = {Maximal subsemigroups containing a particular semigroup}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57465}, year = {2012}, abstract = {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.}, language = {en} }