Affiliation:
1. Department of Mathematics, University of Delhi, Delhi, India
Abstract
Let [Formula: see text] be commutative rings with identity such that [Formula: see text]. A ring extension [Formula: see text] is called a [Formula: see text]-extension of rings if [Formula: see text] is a subring of [Formula: see text] for each pair of subrings [Formula: see text] of [Formula: see text] containing [Formula: see text]. In this paper, a characterization of integrally closed [Formula: see text]-extension of rings is given. The equivalence of [Formula: see text]-extension of rings and [Formula: see text]-extension of rings is established for an integrally closed extension of a local ring. Over a finite dimensional, integrally closed extension of local rings, the equivalence of [Formula: see text]-extensions of rings, FIP, and FCP is shown. Let [Formula: see text] be a subring of [Formula: see text] such that [Formula: see text] is invariant under action by [Formula: see text], where [Formula: see text] is a subgroup of the automorphism group of [Formula: see text]. If [Formula: see text] is a [Formula: see text]-extension of rings, then [Formula: see text] is a [Formula: see text]-extension of rings under some conditions. Many such [Formula: see text]-invariant properties are also discussed.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
2 articles.
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1. Pairs of rings invariant under group action;Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry;2020-01-13
2. The number of intermediate rings in FIP extension of integral domains;Journal of Algebra and Its Applications;2019-11-05