Translatability and translatable semigroups-Reference-Cited by-同舟云学术

Translatability and translatable semigroups

Published:2018-11-05 Issue:1 Volume:16 Page:1266-1282
ISSN:2391-5455
Container-title:Open Mathematics
language:
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Author:

Dudek Wieslaw A.¹,Monzo Robert A. R.²

Affiliation:

1. Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, 50-370Wroclaw, Poland

2. Flat 10, Albert Mansions, Crouch Hill, LondonN8 9RE, United Kingdom

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/downloadpdf/journals/math/16/1/article-p1266.xml

Reference5 articles.

1. On the fine structure of quadratical quasigroups;Quasigroups and Related Systems,2016

2. Quadratical quasigroups;Quasigroups and Related Systems,1997

3. Quadratical groupoids;Note di Matematica,1993

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