Semiring identities in the semigroup B₀

2023/05/27 by V. Yu. Shaprynskiǐ, Shaprynskiǐ, Vyacheslav Yu. · 2 citations
Computer Science · Decision Sciences · #08B15 #16Y60 #20M18 #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2305.17466

openalex publication_date 2023/05/27 · openalex created_date 2023/05/31 · openalex updated_date 2026/07/28

Abstract

The semigroup B₀ is the only, up to isomorphism, 4-element subsemigroup of the 5-element Brandt semigroup B₂. Being an inverse semigroup, the semigroup B₂ can naturally be considered an additively idempotent semiring and B₀ is its subsemiring. We show that the semiring B₀ has a finite basis of identities.

Cited by

• Every additively idempotent semiring satisfying xy≈ xz is finitely based
• The flat semirings with nilpotent multiplicative reducts

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