most citedThe finite basis problem for additively idempotent semirings that relate to S_7

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math.GR2025

Embedding lattices of quasivarieties of periodic groups into lattices of additively idempotent semiring varieties: An algebraic proof

Miaomiao Ren, Xianzhong Zhao, Mikhail V. Volkov

A general result by Jackson (Flat algebras and the translation of universal Horn logic to equational logic, J. Symb. Log. 73(1) (2008) 90--128) implies that the lattice of all quas…

math.GR2025★ 1 cited

The finite basis problem for additively idempotent semirings that relate to S_7

Zidong Gao, Marcel Jackson, Miaomiao Ren +1

The -element additively idempotent semiring is a nonnitely based algebra of the smallest possible order. In this paper we study the nite basis problem for some additively…

math.GR2023★ 2 cited

The additively idempotent semiring is nonfinitely based

Yanan Wu, Miaomiao Ren, Xianzhong Zhao

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