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

2024/07/22 by Ren, Miaomiao, Liu, Junyang, Zeng, Lingli +1 · 3 citations
#03C05 #08B05 #16Y60 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2407.15342

Abstract

We study the finite basis problem for 4-element additively idempotent semirings whose additive reducts are semilattices of height 1. Up to isomorphism, there are 58 such algebras. We show that 49 of them are finitely based and the remaining ones are nonfinitely based.

Cited by

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

Related

• The finite basis problem for additively idempotent semirings of order four, III
• The finite basis problem for additively idempotent semirings of order four, II
• The finite basis problem for additively idempotent semirings that relate to S₇
• Every additively idempotent semiring satisfying xy≈ xz is finitely based
• The additively idempotent semiring S₇⁰ is nonfinitely based