collaborators

6 papers

math.CO2026

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…

math.GR2026

The flat semirings with nilpotent multiplicative reducts

Zidong Gao, Miaomiao Ren

In this paper, we focus on the variety generated by all flat semirings with -nilpotent multiplicative reducts. By introducing graph semirings, we characterize al…

math.RA2026

A finitely based finite semiring generates a variety with continuum many subvarieties

Zidong Gao

This paper establishes the existence of a finitely based finite semiring whose variety contains a continuum of subvarieties; such a variety is said to be of type \(2^{\aleph_0}\).…

math.RA2026

Two nonfinitely based additively idempotent semirings of order four

Mengya Yue, Miaomiao Ren, Zidong Gao

We establish two sufficient conditions for an additively idempotent semiring to be nonfinitely based. As applications, we prove that two specific -element additively idempotent…

math.RA2026

The Interval of Semiring Varieties Has the Cardinality of the Continuum

Zidong Gao, Miaomiao Ren, Mengya Yue

We prove that the interval in the lattice of additively idempotent semiring (ai-semiring) varieties has the cardinality of the continuum,where…

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…