10 papers · 1 filter
The finite basis problem for flat semirings , and
Zidong Gao, Miaomiao Ren, Yilin Zhou
We study the finite basis problem for flat semirings of the forms \(S_c(W)\), \(M_c(W)\), and \(M(W)\), where \(W\) is a nonempty set of words in a free commutative semigroup, a fr…
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 -element additively idempotent semirings. These algebras are divided into five types according to th…
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…
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…
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…
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…
Every additively idempotent semiring satisfying is finitely based
Mengya Yue, Miaomiao Ren
We study the finite basis problem for additively idempotent semirings satisfying the identity . Let denote the variety of all such semirings. Yue et al.…
The flat semirings with nilpotent multiplicative reducts
Zidong Gao, Miaomiao Ren
In this paper, we focus on the variety generated by all flat semirings with -nilpotent multiplicative reducts. By introducing graph semirings, we characterize al…
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 -element additively idempotent semirings whose additive reducts have two minimal elements and one coatom. Up to isomorphism, there are $112…
The finite basis problem for additively idempotent semirings of order four, I
Miaomiao Ren, Junyang Liu, Lingli Zeng +1
We study the finite basis problem for 4-element additively idempotent semirings whose additive reducts are semilattices of height 1. Up to isomorphism, there are 58 such algebras.…