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Schanuel Nullstellensatz for Zilber fields

Paola D'Aquino, Angus Macintyre, Giuseppina Terzo (2010)

Fundamenta Mathematicae

We characterize the unsolvable exponential polynomials over the exponential fields introduced by Zilber, and deduce Picard's Little Theorem for such fields.

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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