The flat semirings with nilpotent multiplicative reducts

2025/06/29 by Gao, Zidong, Ren, Miaomiao
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2506.23047

Abstract

In this paper, we focus on the variety NF₃ generated by all flat semirings with 3-nilpotent multiplicative reducts. By introducing graph semirings, we characterize all subdirectly irreducible members of NF₃. We prove that the variety NF₃ has uncountably many subvarieties and show that every finitely generated subvariety of NF₃ is a Cross variety. Moreover, we demonstrate that NF₃ has a unique limit subvariety, which is generated by all acyclic graph semirings.

Citations

• The finite basis problem for additively idempotent semirings of order four, III
• The finite basis problem for additively idempotent semirings that relate to S₇
• The finite basis problem for additively idempotent semirings of order four, II
• The finite basis problem for additively idempotent semirings of order four, I
• Semiring identities in the semigroup B₀
• Nonfinitely based ai-semirings with finitely based semigroup reducts
• Semiring identities of the Brandt monoid
• On Absolute Algebraic Geometry, the affine case

Related

• The varieties generated by 3-hypergraph semirings
• On the variety generated by all semirings of order two
• Flat extensions of groups and limit varieties of ai-semirings
• Every additively idempotent semiring satisfying xy≈ xz is finitely based
• The finite basis problem for additively idempotent semirings that relate to S₇