2 citations · 3 across the 8 of their papers we have counts for
8 papers
A Continuum in the Lattice of Semiring Varieties: The Interval
Zidong Gao, Miaomiao Ren, Xianzhong Zhao
For an additively idempotent semiring (ai-semiring) , let denote the ai-semiring obtained from by adjoining a new element . In this paper, we develop an approach to…
The finite basis problem for the flat semirings
Zidong Gao, Miaomiao Ren, Xianzhong Zhao
We focus on the finite basis problem for flat semirings of the form , where is an arbitrary set of nonempty words. We prove that generates a Cross variety (and hen…
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…
Nonfinitely based ai-semirings with finitely based semigroup reducts
Marcel Jackson, Miaomiao Ren, Xianzhong Zhao
We present some general results implying nonfinite axiomatisability of many additively idempotent semirings with finitely based semigroup reducts. The smallest is a -element com…