On Bezout and distributive generalized power series rings

[摘要] In this paper we give sufficient and necessary conditions on a strongly regular ring of coefficients R and a monoid of nonnegative exponents S such that the generalized power series ring R [S] is right Bezout. It is shown that all such generalized power series rings are right distributive. We also study when a generalized power series ring over a von Neumann regular ring has weak dimension less than or equal to one. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] generalized power series ring;right Bezout ring;right distributive ring;weak dimension;orthogonally finite ring;von Neumann regular ring;strongly regular ring;right semihereditary ring;right chain ring;right chain monoid