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Some nil-ai-semiring varieties.
- Source :
-
Semigroup Forum . Feb2024, Vol. 108 Issue 1, p258-271. 14p. - Publication Year :
- 2024
-
Abstract
- We study some nil-ai-semiring varieties. We establish a model for the free object in the variety FC generated by all commutative flat semirings. Also, we provide two sufficient conditions under which a finite ai-semiring is nonfinitely based. As a consequence, we show that the power semiring P S ˙ c (W) of the finite nil-semigroup S ˙ c (W) is nonfinitely based, where W is a finite set of words in the free commutative semigroup X c + over an alphabet X, whenever the maximum of lengths of words in W is k ≥ 3 and W does not contain the kth power of a letter. This partially answers a problem raised by Jackson et al. (J Algebr 611: 211–245, 2022). [ABSTRACT FROM AUTHOR]
- Subjects :
- *VOCABULARY
Subjects
Details
- Language :
- English
- ISSN :
- 00371912
- Volume :
- 108
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Semigroup Forum
- Publication Type :
- Academic Journal
- Accession number :
- 176119898
- Full Text :
- https://doi.org/10.1007/s00233-024-10411-3