Affiliation:
1. University of Bahrain, Faculty of Science, Department of Mathematics, P. O. Box: 32038, Sukhir, Kingdom of Bahrain
Abstract
An overring [Formula: see text] of an integral domain [Formula: see text] is said to be comparable if [Formula: see text], [Formula: see text], and each overring of [Formula: see text] is comparable to [Formula: see text] under inclusion. We do provide necessary and sufficient conditions for which [Formula: see text] has a comparable overring. Several consequences are derived, specially for minimal overrings, or in the case where the integral closure [Formula: see text] of [Formula: see text] is a comparable overring, or also when each chain of distinct overrings of [Formula: see text] is finite.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
3 articles.
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1. On ring extensions pinched at the integral closure;Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry;2024-05-26
2. Comparable overrings of a commutative ring;Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry;2023-12-04
3. Splitting ring extensions;Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry;2022-06-17