Ilan Levin

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20242026

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3 papers · 1 filter

math.RA2026

General Polynomials and Eigenvalues Over Cayley--Dickson Algebras

Adam Chapman, Ilan Levin, Solomon Vishkautsan

In this paper, we provide an explicit method for determining the zero set of monic quadratic general polynomials over Cayley--Dickson algebras with any base field of characteristic…

math.RA2026

Central Products of Cayley-Dickson Loops

Adam Chapman, Ilan Levin

This paper studies the triviality of commutators in central products of Cayley-Dickson loops. Two immediate outcomes of this study are (1) the construction of a sequence of non-com…

math.RA2026

Cyclic Division Algebras of Odd Prime Degree are never Amitsur-Small

Adam Chapman, Ilan Levin, Marco Zaninelli

A division ring $D$ is Amitsur-Small if for every $n$ and every maximal left ideal $I$ in $D [x_{1}, \dots, x_{n}]$ , $I \cap D [x_{1}, \dots, x_{n - 1}]$ is maximal in $D [x_{1}, \dots, x_{n - 1}]$ . Th…