Abhyankar proved that every field of finite transcendence degree over or over a finite field is a homomorphic image of a subring of the ring of polynomials (for some depending on the field). We conjecture that his result cannot be substantially strengthened and show that our conjecture implies a well-known conjecture on the additive idempotence of semifields that are finitely generated as semirings.
Recently, we have shown that a semiring is completely regular if and only if is a union of skew-rings. In this paper we show that a semiring satisfying can be embedded in a completely regular semiring if and only if is additive separative.
A ring or an idempotent semiring is associative provided that additive endomorphisms are multiplicative.
This short note is a continuation of and and its purpose is to show that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced in the sense of .
We introduce sturdy frames of type (2,2) algebras, which are a common generalization of sturdy semilattices of semigroups and of distributive lattices of rings in the theory of semirings. By using sturdy frames, we are able to characterize some semirings. In particular, some results on semirings recently obtained by Bandelt, Petrich and Ghosh can be extended and generalized.