Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2012; 49(5): 1067-1079

Printed September 30, 2012

https://doi.org/10.4134/BKMS.2012.49.5.1067

Copyright © The Korean Mathematical Society.

Uniform and couniform dimension of generalized inverse polynomial modules

Renyu Zhao

Northwest Normal University

Abstract

Let $M$ be a right $R$-module, $(S,\leq)$ a strictly totally ordered monoid which is also artinian and $\omega:S\longrightarrow {\rm Aut}(R)$ a monoid homomorphism, and let $[M^{S,\leq}]_{[[R^{S,\leq},\omega]]}$ denote the generalized inverse polynomial module over the skew generalized power series ring $[[R^{S,\leq},\omega]]$. In this paper, we prove that $[M^{S,\leq}]_{[[R^{S,\leq},\omega]]}$ has the same uniform dimension as its coefficient module $M_R$, and that if, in addition, $R$ is a right perfect ring and $S$ is a chain monoid, then $[M^{S,\leq}]_{[[R^{S,\leq},\omega]]}$ has the same couniform dimension as its coefficient module $M_R$.

Keywords: skew generalized power series ring, generalized inverse polynomial module, uniform dimension, couniform dimension

MSC numbers: Primary 16W60

Stats or Metrics

Share this article on :

Related articles in BKMS