5 papers
Two nonfinitely based additively idempotent semirings of order four
Mengya Yue, Miaomiao Ren, Zidong Gao
We establish two sufficient conditions for an additively idempotent semiring to be nonfinitely based. As applications, we prove that two specific -element additively idempotent…
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 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…