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Finitely Σ-CS Property of Excellent Extensions of Rings

Finitely Σ-CS Property of Excellent Extensions of Rings For a right excellent extension S of a ring R, it is proved that R is right, finitely Σ-CS if and only if S is the same. As an application of this result, a number of examples of group rings which are finitely Σ-CS are presented. This generalizes a result of Jain, et al. [5], where it was shown that F[D ∞] is CS when F is a field of characteristic ≠ 2. It is also proved that if R is a commutative domain with 2−1 ∈ R and C2 is the cyclic group of order 2, then R[C 2] is a CS-ring. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebra Colloquium Springer Journals

Finitely Σ-CS Property of Excellent Extensions of Rings

Parmenter, M.; Zhou, Yiqiang
Algebra Colloquium , Volume 10 (1) – Jan 1, 2003
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Publisher
Springer Journals
Copyright
Copyright © 2003 by AMSS CAS
Subject
Mathematics; Algebra; Algebraic Geometry
ISSN
1005-3867
eISSN
0219-1733
DOI
10.1007/s100110300003
Publisher site
See Article on Publisher Site

Abstract

For a right excellent extension S of a ring R, it is proved that R is right, finitely Σ-CS if and only if S is the same. As an application of this result, a number of examples of group rings which are finitely Σ-CS are presented. This generalizes a result of Jain, et al. [5], where it was shown that F[D ∞] is CS when F is a field of characteristic ≠ 2. It is also proved that if R is a commutative domain with 2−1 ∈ R and C2 is the cyclic group of order 2, then R[C 2] is a CS-ring.

Journal

Algebra Colloquium – Springer Journals

Published: Jan 1, 2003

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