Miaomiao Ren

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20242026

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5 papers · 1 filter

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.RA2026

A nonfinitely based additively idempotent semiring that is not strongly nonfinitely based and generates a limit variety

Xiaolei Shao, Miaomiao Ren, Zidong Gao

We present an explicit infinite equational basis for the six-element additively idempotent semiring $T R_{6}$ and prove that $T R_{6}$ is nonfinitely based. We also give a complete descr…

math.RA2026

The finite basis problem for matrix semirings $M_{n} (S_{7})$

Jun Jiao, Miaomiao Ren

We first prove that two matrix semirings $M_{n} (S_{1})$ and $M_{n} (S_{2})$ are equationally equivalent whenever additively idempotent semirings $S_{1}$ and $S_{2}$ are equati…

math.RA2026

The finite basis problem for matrix semirings over a two-element additively idempotent semiring

Jun Jiao, Miaomiao Ren

We provide a complete classification of matrix semirings $M_{n} (S)$ over two-element additively idempotent semirings $S$ with respect to the finite basis property.Our main t…

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…

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

A nonfinitely based additively idempotent semiring that is not strongly nonfinitely based and generates a limit variety

The finite basis problem for matrix semirings Mn​(S7​)

The finite basis problem for matrix semirings over a two-element additively idempotent semiring

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

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

The finite basis problem for matrix semirings $M_{n} (S_{7})$

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