Mengya Yue

collaborators

18 papers

math.GR2026

Two-element factors and finite bases for additively idempotent semirings

Qirui Ma, Mengya Yue

For every additively idempotent semiring $S$ in the constant-free signature, $S$ is finitely based if and only if $S \times E$ is finitely based when $E = M_{2}$ or $T_{2}$ . For each $E\i…

math.GR2026

The finite basis problem and subvariety intervals for max-plus matrix semirings

Jun Jiao, Mengya Yue

Let $S = (N, max, +)$ be the max-plus algebra of the nonnegative integers, and let $S$ be obtained from $S$ by adjoining $- \infty$ as a semiring zero. We first prove that t…

math.RA2026

Strong nonfinite basability of the three-element flat semiring $S_{7}$

Mengya Yue, Xiaolei Shao

We prove that the three-element flat semiring $S_{7}$ is strongly nonfinitely based within the class of additively idempotent semirings. More generally, let $N$ be the subva…

math.GR2026

The finite basis problem for additively idempotent semirings of order four, IV

Miaomiao Ren, Mengya Yue, Mengyu Yuan +3

This paper is the fourth in a series devoted to the finite basis problem for $4$ -element additively idempotent semirings. These algebras are divided into five types according to th…

math.GR2026

Inherently nonfinitely based additively idempotent semirings

Miao Miao Ren, Meng Ya Yue, Yi Lin Zhou

We establish a sufficient condition for an additively idempotent semiring to be inherently nonfinitely based: if its generated variety is locally finite and every Zimin word is min…

math.RA2026

The six-element additively idempotent semiring $B_{2}^{1}$ is inherently nonfinitely based

Miao Miao Ren, Meng Ya Yue, Yi Lin Zhou

We show that the six-element additively idempotent semiring $B_{2}^{1}$ is inherently nonfinitely based. More precisely, for every positive integer $n$ , we construct an infinite additi…

math.GR2026

The unique limit subvariety of the max-plus variety and finite basis properties

Xiaolei Shao, Mengya Yue

We prove that the variety generated by the max-plus algebra on the nonnegative integers has a unique limit subvariety, namely the variety generated by the six-element semiring cons…

math.GR2026

The finite basis problem for all subvarieties of the variety $V (S_{7}^{0})$

Mengya Yue

We solve the finite basis problem for all subvarieties of $V (S_{7}^{0})$ . By considering their intersections with $V (S_{7})$ , we reduce the problem to six intervals. We…

math.GR2026

The variety generated by all additively idempotent semirings of order four

Mengya Yue, Xiaolei Shao

We prove that the variety generated by all four-element additively idempotent semirings has no finite basis for its identities.

math.GR2026

Explicit equational bases for the power semirings of $S_{7}$

Mengya Yue, Miaomiao Ren, Zidong Gao

For every semigroup $S$ , the set $P (S)$ of all subsets of $S$ and the set $P^{+} (S)$ of all nonempty subsets of $S$ form additively idempotent semirings under s…

math.GR2026

The finite basis problem for the power semirings of finite groups

Zidong Gao, Miaomiao Ren, Xiaolei Shao +1

For any group $G$ , the set of all nonempty subsets of $G$ forms an additively idempotent semiring under set-theoretic union and elementwise multiplication, called the power semirin…

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.RA2026

A new limit variety of additively idempotent semirings

Simin Lyu, Miaomiao Ren, Mengya Yue

We establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. Applying this condition, we prove that the six-element additively idempotent semi…

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 $4$ -element additively idempotent…

math.RA2026

The Interval $[V (S_{7}), V (B_{2}^{1})]$ of Semiring Varieties Has the Cardinality of the Continuum

Zidong Gao, Miaomiao Ren, Mengya Yue

We prove that the interval $[V (S_{7}), V (B_{2}^{1})]$ in the lattice of additively idempotent semiring (ai-semiring) varieties has the cardinality of the continuum,where…

math.GR2025

Every additively idempotent semiring satisfying $x y \approx x z$ is finitely based

Mengya Yue, Miaomiao Ren

We study the finite basis problem for additively idempotent semirings satisfying the identity $x y \approx x z$ . Let $R$ denote the variety of all such semirings. Yue et al.…

math.GR2025

The finite basis problem for additively idempotent semirings of order four, III

Miaomiao Ren, Zexi Liu, Mengya Yue +1

We study the finite basis problem for $4$ -element additively idempotent semirings whose additive reducts have two minimal elements and one coatom. Up to isomorphism, there are $112…

math.GR2025

The finite basis problem for additively idempotent semirings of order four, II

Mengya Yue, Miaomiao Ren, Lingli Zeng +1

We study the finite basis problem for $4$ -element additively idempotent semirings whose additive reducts are quasi-antichains. Up to isomorphism, there are $93$ such algebras. We s…

Two-element factors and finite bases for additively idempotent semirings

The finite basis problem and subvariety intervals for max-plus matrix semirings

Strong nonfinite basability of the three-element flat semiring S7​

The finite basis problem for additively idempotent semirings of order four, IV

Inherently nonfinitely based additively idempotent semirings

The six-element additively idempotent semiring B21​ is inherently nonfinitely based

The unique limit subvariety of the max-plus variety and finite basis properties

The finite basis problem for all subvarieties of the variety V(S70​)

The variety generated by all additively idempotent semirings of order four

Explicit equational bases for the power semirings of S7​

The finite basis problem for the power semirings of finite groups

A nonfinitely based additively idempotent semiring of order four

A new limit variety of additively idempotent semirings

Two nonfinitely based additively idempotent semirings of order four

The Interval [V(S7​),V(B21​)] of Semiring Varieties Has the Cardinality of the Continuum

Every additively idempotent semiring satisfying xy≈xz is finitely based

The finite basis problem for additively idempotent semirings of order four, III

The finite basis problem for additively idempotent semirings of order four, II

Strong nonfinite basability of the three-element flat semiring $S_{7}$

The six-element additively idempotent semiring $B_{2}^{1}$ is inherently nonfinitely based

The finite basis problem for all subvarieties of the variety $V (S_{7}^{0})$

Explicit equational bases for the power semirings of $S_{7}$

The Interval $[V (S_{7}), V (B_{2}^{1})]$ of Semiring Varieties Has the Cardinality of the Continuum

Every additively idempotent semiring satisfying $x y \approx x z$ is finitely based