Translatability and translatable semigroups
Rings and Algebras
2017-11-08 v1
Abstract
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-translatable groupoids 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 of disjoint copies of cyclic groups of the same order. Methods of constructing k-translatable semigroups that are not left cancellative are given.
Cite
@article{arxiv.1711.02561,
title = {Translatability and translatable semigroups},
author = {Wieslaw A. Dudek and Robert A. R. Monzo},
journal= {arXiv preprint arXiv:1711.02561},
year = {2017}
}
Comments
22 pages. This paper has recently been submitted to Semigroup Forum