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...
Main Authors: | , |
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Format: | Article |
Language: | English |
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De Gruyter
2018-11-01
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Series: | Open Mathematics |
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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. |
first_indexed | 2024-12-17T19:19:58Z |
format | Article |
id | doaj.art-3d784ba0e18e436baa61c53a254cc675 |
institution | Directory Open Access Journal |
issn | 2391-5455 |
language | English |
last_indexed | 2024-12-17T19:19:58Z |
publishDate | 2018-11-01 |
publisher | De Gruyter |
record_format | Article |
series | Open Mathematics |
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 |