English

Semiring identities in the semigroup $B_2$

Group Theory 2026-04-03 v1

Abstract

The 5-element Brandt semigroup B2B_2 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.

Keywords

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

R2 v1 2026-07-01T11:50:28.548Z