most citedThe finite basis problem for additively idempotent semirings that relate to S_7

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math.RA2026

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…

math.RA2026

A finitely based finite semiring generates a variety with continuum many subvarieties

Zidong Gao

This paper establishes the existence of a finitely based finite semiring whose variety contains a continuum of subvarieties; such a variety is said to be of type \(2^{\aleph_0}\).…

math.RA2026

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…

math.RA2026

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…