|
Algebra and Discrete Mathematics, 2019, том 27, выпуск 1, страницы 144–154
(Mi adm698)
|
|
|
|
Эта публикация цитируется в 1 научной статье (всего в 1 статье)
RESEARCH ARTICLE
Representations of ordered doppelsemigroups by binary relations
Yurii V. Zhuchoka, Jörg Koppitzb a Luhansk Taras Shevchenko National University, Gogol square 1, Starobilsk, Ukraine, 92703
b Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev St, Bl. 8, 1113 Sofia, Bulgaria
Аннотация:
We extend the study of doppelsemigroups and introduce the notion of an ordered doppelsemigroup. We construct the ordered doppelsemigroup of binary relations on an arbitrary set and prove that every ordered doppelsemigroup is isomorphic to some ordered doppelsemigroup of binary relations. In particular, we obtain an analogue of Cayley's theorem for semigroups in the class of doppelsemigroups. We also describe the representations of ordered doppelsemigroups by binary transitive relations.
Ключевые слова:
doppelsemigroup, ordered doppelsemigroup, semigroup, binary relation, representation.
Поступила в редакцию: 27.11.2018
Образец цитирования:
Yurii V. Zhuchok, Jörg Koppitz, “Representations of ordered doppelsemigroups by binary relations”, Algebra Discrete Math., 27:1 (2019), 144–154
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm698 https://www.mathnet.ru/rus/adm/v27/i1/p144
|
|