15 papers
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…
The six-element additively idempotent semiring is inherently nonfinitely based
Miao Miao Ren, Meng Ya Yue, Yi Lin Zhou
We show that the six-element additively idempotent semiring is inherently nonfinitely based. More precisely, for every positive integer , we construct an infinite additi…
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…
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 and prove that is nonfinitely based. We also give a complete descr…
The finite basis problem for matrix semirings
Jun Jiao, Miaomiao Ren
We first prove that two matrix semirings and are equationally equivalent whenever additively idempotent semirings and are equati…
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…
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 over two-element additively idempotent semirings with respect to the finite basis property.Our main t…
The Interval of Semiring Varieties Has the Cardinality of the Continuum
Zidong Gao, Miaomiao Ren, Mengya Yue
We prove that the interval in the lattice of additively idempotent semiring (ai-semiring) varieties has the cardinality of the continuum,where…
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.…