13 papers · 1 filter
Two-element factors and finite bases for additively idempotent semirings
Qirui Ma, Mengya Yue
For every additively idempotent semiring in the constant-free signature, is finitely based if and only if is finitely based when or . For each $E\i…
The finite basis problem and subvariety intervals for max-plus matrix semirings
Jun Jiao, Mengya Yue
Let be the max-plus algebra of the nonnegative integers, and let be obtained from by adjoining as a semiring zero. We first prove that t…
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 unique limit subvariety of the max-plus variety and finite basis properties
Xiaolei Shao, Mengya Yue
We prove that the variety generated by the max-plus algebra on the nonnegative integers has a unique limit subvariety, namely the variety generated by the six-element semiring cons…
The finite basis problem for all subvarieties of the variety
Mengya Yue
We solve the finite basis problem for all subvarieties of . By considering their intersections with , we reduce the problem to six intervals. We…
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.
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…
A nonfinitely based additively idempotent semiring of order four
Mengya Yue, Miaomiao Ren
We first establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. As applications, we exhibit several examples of additively idempotent semir…
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 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, II
Mengya Yue, Miaomiao Ren, Lingli Zeng +1
We study the finite basis problem for -element additively idempotent semirings whose additive reducts are quasi-antichains. Up to isomorphism, there are such algebras. We s…