Semiring identities in the semigroup $B_2$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918425374228480 |
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| author | Shaprynskiǐ, Vyacheslav Yu. |
| author_facet | Shaprynskiǐ, Vyacheslav Yu. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_01706 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semiring identities in the semigroup $B_2$ Shaprynskiǐ, Vyacheslav Yu. Group Theory 08B05, 16Y60, 20M18 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. |
| title | Semiring identities in the semigroup $B_2$ |
| topic | Group Theory 08B05, 16Y60, 20M18 |
| url | https://arxiv.org/abs/2604.01706 |