most citedThe finite basis problem for additively idempotent semirings that relate to S_7

1 citations · 1 across the 11 of their papers we have counts for

collaborators
Showing math.GRShow all

8 papers · 1 filter

math.GR2026

Finite Bases for Truncated Cyclic Group Flat Semirings with Two Independent Parameters

Qirui Ma, Zidong Gao

For positive integers \(m,n\), let \[ A_{m,n}=(\{1,\ldots,m\}\times\Z_n)\cup\{0\} \] have flat addition and multiplication truncated at degree \(m\). We prove that \(A_{m,n}\) is f…

math.GR2026

Finite bases and joins for semirings defined by the divisibility order

Xiaolei Shao, Zidong Gao

We study additively idempotent semirings obtained from commutative words by equipping their subwords with the divisibility order. Every finite semiring associated with a power of o…

math.GR2026

Nonfinitely based intervals of power semiring varieties

Xiaolei Shao, Zidong Gao

We study intervals in the lattice of additively idempotent semiring varieties associated with power semirings of finite groups. We prove that every variety lying above the nonempty…

math.GR2026

A Continuum in the Lattice of Semiring Varieties: The Interval

Zidong Gao, Miaomiao Ren, Xianzhong Zhao

For an additively idempotent semiring (ai-semiring) , let denote the ai-semiring obtained from by adjoining a new element . In this paper, we develop an approach to…

math.GR2026

Explicit equational bases for the power semirings of

Mengya Yue, Miaomiao Ren, Zidong Gao

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