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2020•Journal of Algebra and Its ApplicationsRequires access

Pairs of domains where most of the intermediate domains are Prüfer

Noômen Jarboui

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Abstract

Let [Formula: see text] be an extension of integral domains. The ring [Formula: see text] is said to be maximal non-Prüfer subring of [Formula: see text] if [Formula: see text] is not a Prüfer domain, while each subring of [Formula: see text] properly containing [Formula: see text] is a Prüfer domain. Jaballah has characterized this kind of ring extensions in case [Formula: see text] is a field [A. Jaballah, Maximal non-Prüfer and maximal non-integrally closed subrings of a field, J. Algebra Appl. 11(5) (2012) 1250041, 18 pp.]. The aim of this paper is to deal with the case where [Formula: see text] is any integral domain which is not necessarily a field. Several examples are provided to illustrate our theory.

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What this paper is about

Let [Formula: see text] be an extension of integral domains. The ring [Formula: see text] is said to be maximal non-Prüfer subring of [Formula: see text] if [Formula: see text] is not a Prüfer domain, while each subring of [Formula: see text] properly containing [Formula: see text] is a Prüfer domain. Jaballah has characterized this kind of ring extensions in case [Formula: see text] is a field [A. Jaballah, Maximal non-Prüfer and maximal non-integrally closed subrings of a field, J. Algebra Appl. 11(5) (2012) 1250041, 18 pp.]. The aim of this paper is to deal with the case where [Formula: see text] is any integral domain which is not necessarily a field. Several examples are provided to illustrate our theory.

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Available abstract

Let [Formula: see text] be an extension of integral domains. The ring [Formula: see text] is said to be maximal non-Prüfer subring of [Formula: see text] if [Formula: see text] is not a Prüfer domain, while each subring of [Formula: see text] properly containing [Formula: see text] is a Prüfer domain. Jaballah has characterized this kind of ring extensions in case [Formula: see text] is a field [A. Jaballah, Maximal non-Prüfer and maximal non-integrally closed subrings of a field, J. Algebra Appl. 11(5) (2012) 1250041, 18 pp.]. The aim of this paper is to deal with the case where [Formula: see text] is any integral domain which is not necessarily a field. Several examples are provided to illustrate our theory.

Key concepts: Subring, Integral domain, Mathematics, Integrally closed, Domain (mathematical analysis), Ring (chemistry), Field (mathematics), Extension (predicate logic)

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