On a problem of Amitsur and Small

2024/12/09 by Elad Paran, Paran, Elad
Computer Science · Engineering · #Optimization and Variational Analysis #Aerospace Engineering and Control Systems #Optimization and Packing Problems

paper · pdf · doi:10.48550/arxiv.2412.06230

Abstract

We construct an example of a division ring D and a maximal left ideal M in the polynomial ring D[x,y] in two central variables over D, such that the intersection M ∩ D[x] is not a maximal left ideal in D[x]. This resolves a ring-theoretic problem of Amitsur and Small raised in 1978.

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