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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…
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…
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…
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),…
Flat extensions of groups and limit varieties of ai-semirings
Miaomiao Ren, Marcel Jackson, Xianzhong Zhao +1
The present paper is a continuation of \cite{jrz} and is devoted to the study of limit varieties of additively idempotent semirings. A limit variety is a nonfinitely based variety…
The Burnside ai-semiring variety defined by
Miaomiao Ren, Xianzhong Zhao, Mikhail V. Volkov
Let denote the ai-semiring variety defined by the identity , where . We characterize all subdirectly irreducible members of a semisimple subvari…