Jun Jiao

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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.GR2026

Matrix varieties over $S_{7}$ : dimension-three stability and continuum-sized subvariety intervals

Jun Jiao, Xiaolei Shao

We study matrix semirings over the three-element flat additively idempotent semiring with elements one, a, and infinity, where the square of a is infinity. We determine the associa…

math.GR2026

The finite basis problem for $2 \times 2$ triangular Boolean matrix semirings and incidence semirings

Jun Jiao, Xiaolei Shao

An explicit finite identity basis is given for the eight-element semiring of upper triangular Boolean $2\times2$ matrices in the signature $(+,\cdot)$. The basis consists of a…

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

Matrix varieties over S7​: dimension-three stability and continuum-sized subvariety intervals

The finite basis problem for 2×2 triangular Boolean matrix semirings and incidence semirings

Matrix varieties over $S_{7}$ : dimension-three stability and continuum-sized subvariety intervals

The finite basis problem for $2 \times 2$ triangular Boolean matrix semirings and incidence semirings