Finitely Σ-CS Property of Excellent Extensions of Rings

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 2−1R and C2 is the cyclic group of order 2, then R[C2] is a CS-ring.

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Correspondence to M. M. Parmenter.

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2000 Mathematics Subject Classification: 16S20, 16D50

The research was supported by the NSERC of Canada, grants A8775 and OGP0194196.

Communicated by Weimin Xue

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Parmenter, M.M., Zhou, Y. Finitely Σ-CS Property of Excellent Extensions of Rings. Algebra Colloq. 10, 17–21 (2003). https://doi.org/10.1007/s100110300003

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Keywords:

  • excellent extensions
  • CS-rings
  • finitely Σ-CS rings