Quelques Propriétés d'UNE Extension Minimale

Oukessou, Mohamed; Miri, Abderrahim

doi:10.1081/agb-100001538

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2009

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“…In [DS07], Dobbs and Shapiro examined the commutative minimal extensions of certain non-domains, and (in a certain sense) reduced the study of commutative minimal extensions to extensions of reduced rings. Other aspects of commutative minimal extensions are studied in [PL96], [PPL06], [Sze50], [Aya03], [Dob06], [Dob07], [Pap76], [OM99], [OM01], [OM03], [Ouk06], as well as others. Minimal extensions of arbitrary rings, as well as minimal noncommutative extensions of commutative rings, have received considerably less attention than their commutative counterparts.…”

Section: Introductionmentioning

confidence: 99%

On Minimal Extensions of Rings

Dorsey

Mesyan

2009

Communications in Algebra

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Given two rings R ⊆ 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. * 2000 Mathematics Subject Classification numbers: 16S70 (primary), 16S20, 16N60(secondary).

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