On minimal extensions of rings

Details On minimal extensions of rings On minimal extensions of rings

2008-05-21

arxiv.org/abs/0805.3370v1

Comm. Algebra 37 (2009) 3463-3486

Mathematics

Rings and Algebras

25 pages

Scientific paper

10.1080/00927870802502910

Given two rings $R \subseteq S$, $S$ is said to be a minimal ring extension of $R$ if $R$ is a maximal subring of $S$. In this article, we study minimal extensions of an arbitrary ring $R$, with particular focus on those possessing nonzero ideals that intersect $R$ trivially. We will also classify the minimal ring extensions of prime rings, generalizing results of Dobbs, Dobbs & Shapiro, and Ferrand & Olivier on commutative minimal extensions.

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