The additively idempotent semiring S₇⁰ is nonfinitely based

2023/08/06 by Wu, Yanan, Ren, Miaomiao, Zhao, Xianzhong · 2 citations
#03C05 #08B05 #16Y60 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.2308.03101

Abstract

We show that the additively idempotent semiring S₇⁰ has no finite basis for its equational theory. This answers an open problem posed by Jackson et al. (J. Algebra 611 (2022), 211--245).

Cited by

• Every additively idempotent semiring satisfying xy≈ xz is finitely based
• Embedding lattices of quasivarieties of periodic groups into lattices of additively idempotent semiring varieties: An algebraic proof

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• The finite basis problem for additively idempotent semirings of order four, II
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