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Semifields and a theorem of Abhyankar

Vítězslav Kala (2017)

Commentationes Mathematicae Universitatis Carolinae

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 [ T 1 , , T n ] (for some n 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.

Shape tiling.

Keating, Kevin, King, Jonathan L. (1997)

The Electronic Journal of Combinatorics [electronic only]

Simple zeropotent paramedial groupoids are balanced

Robert El Bashir, Jaroslav Ježek, Tomáš Kepka (2000)

Czechoslovak Mathematical Journal

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 .

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