Semiring identities in the semigroup $B_2$
Group Theory
2026-04-03 v1
Abstract
The 5-element Brandt semigroup admits the structure of a naturally semilattice-ordered inverse semigroup, thus becoming an additively idempotent semiring with the operation of taking greatest lower bounds as the semiring addition. For this semiring we present a finite basis of identities and thus, by the previous results, complete the solution of Finite Basis Problem for combinatorial naturally semilattice-ordered inverse semigroups.
Cite
@article{arxiv.2604.01706,
title = {Semiring identities in the semigroup $B_2$},
author = {Vyacheslav Yu. Shaprynskiǐ},
journal= {arXiv preprint arXiv:2604.01706},
year = {2026}
}
Comments
11 pages