Semiring identities of the semigroup B0

The semigroup B 0 is the only 4-element subsemigroup of the 5-element Brandt semigroup B 2 , up to isomorphism. Being an inverse semigroup, the semigroup B 2 can naturally be considered an additively idempotent semiring and B 0 is its subsemiring. We show that the semiring B 0 has a finite basis of...

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Bibliographic Details
Published in:Semigroup forum 2024, Vol.109 (3), p.693-705
Main Author: Shaprynskiǐ, Vyacheslav Yu
Format: Article
Language:English
Subjects:
Algebra
Isomorphism
Mathematics
Mathematics and Statistics
Research Article
Rings (mathematics)
Semigroups
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Summary:The semigroup B 0 is the only 4-element subsemigroup of the 5-element Brandt semigroup B 2 , up to isomorphism. Being an inverse semigroup, the semigroup B 2 can naturally be considered an additively idempotent semiring and B 0 is its subsemiring. We show that the semiring B 0 has a finite basis of identities.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-024-10476-0