Finitely ∑-CS Property of Excellent Extensions of Rings

摘要

For a right excellent extension S of a ring R, it is proved that R is right finitely ∑-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 ∑-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[C2] is a CS-ring.