Xiaolei Shao

collaborators

3 papers

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.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.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…