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math.GR2026
A nonfinitely based additively idempotent semiring of order four
Mengya Yue, Miaomiao Ren
We first establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. As applications, we exhibit several examples of additively idempotent semir…
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
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…