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 |
| Published: |
De Gruyter
2018-11-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2018-0106 |
| Summary: | 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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| ISSN: | 2391-5455 |