Translatability and translatable semigroups

2017/11/06 by Dudek, Wieslaw A., Monzo, Robert A. R.
#20M15 #20N02 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1711.02561

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.

Related

• The structure of idempotent translatable quasigroups
• Translatable quadratical quasigroups
• Groupoids viewed as inverse semigroups
• Semigroups, groups, and algebras of dynamical origin
• Right, left and double division in semigroups that are semilattices of groups