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arXiv · 2604.01706

Semiring identities in the semigroup $B_2$

Vyacheslav Yu. Shaprynskiǐ
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Abstract

The 5-element Brandt semigroup $B_2$ 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.

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Vyacheslav Yu. Shaprynskiǐ. 2026-04-02. Semiring identities in the semigroup $B_2$. https://arxiv.org/abs/2604.01706

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