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Translatability and translatable semigroups

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 05 Nov 2018Embargo end date: 01 Jan 2017Publisher:Walter de Gruyter GmbHJournal:Open Mathematics, volume 16, pages 1,266-1,282 (eissn: 2391-5455,

Authors: Robert A. R. Monzo; Wieslaw A. Dudek;

doi: 10.1515/math-2018-0106 , 10.48550/arxiv.1711.02561

arXiv: http://arxiv.org/abs/1711.02561

Translatability and translatable semigroups

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Abstract

AbstractThe concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatablegroupoids are proved. Necessary and sufficient conditions are found for a left cancellative k-translatable groupoid to be a semigroup. Any such semigroup is proved to be left unitary and a union disjoint copies of cyclic groups of the same order. Methods of constructing k-translatable semigroups that are not left cancellative are given.

Related Organizations

Wrocław University of Science and Technology
Poland

Keywords

translatable semigroup, idempotent, Mathematics - Rings and Algebras, 20m15, 20M15, 20N02, 20n02, Rings and Algebras (math.RA), semigroup, QA1-939, FOS: Mathematics, left cancellative semigroup, Mathematics

2 Research products, page 1 of 1

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