5 papers · 1 filter
Strong nonfinite basability of the three-element flat semiring
Mengya Yue, Xiaolei Shao
We prove that the three-element flat semiring is strongly nonfinitely based within the class of additively idempotent semirings. More generally, let be the subva…
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 new limit variety of additively idempotent semirings
Simin Lyu, Miaomiao Ren, Mengya Yue
We establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. Applying this condition, we prove that the six-element additively idempotent semi…
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…