Translatability and translatable semigroups

The 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...

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Main Authors: Dudek Wieslaw A., Monzo Robert A. R.
Format: Article
Language:English
Published: De Gruyter 2018-11-01
Series:Open Mathematics
Subjects:
Online Access:https://doi.org/10.1515/math-2018-0106
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author Dudek Wieslaw A.
Monzo Robert A. R.
author_facet Dudek Wieslaw A.
Monzo Robert A. R.
author_sort Dudek Wieslaw A.
collection DOAJ
description The 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.
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spelling doaj.art-3d784ba0e18e436baa61c53a254cc6752022-12-21T21:35:35ZengDe GruyterOpen Mathematics2391-54552018-11-011611266128210.1515/math-2018-0106math-2018-0106Translatability and translatable semigroupsDudek Wieslaw A.0Monzo Robert A. R.1Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, 50-370Wroclaw, PolandFlat 10, Albert Mansions, Crouch Hill, LondonN8 9RE, United KingdomThe 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.https://doi.org/10.1515/math-2018-0106semigrouptranslatable semigroupleft cancellative semigroupidempotent20m1520n02
spellingShingle Dudek Wieslaw A.
Monzo Robert A. R.
Translatability and translatable semigroups
Open Mathematics
semigroup
translatable semigroup
left cancellative semigroup
idempotent
20m15
20n02
title Translatability and translatable semigroups
title_full Translatability and translatable semigroups
title_fullStr Translatability and translatable semigroups
title_full_unstemmed Translatability and translatable semigroups
title_short Translatability and translatable semigroups
title_sort translatability and translatable semigroups
topic semigroup
translatable semigroup
left cancellative semigroup
idempotent
20m15
20n02
url https://doi.org/10.1515/math-2018-0106
work_keys_str_mv AT dudekwieslawa translatabilityandtranslatablesemigroups
AT monzorobertar translatabilityandtranslatablesemigroups