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http://dx.doi.org/10.4134/BKMS.2012.49.5.1067

UNIFORM AND COUNIFORM DIMENSION OF GENERALIZED INVERSE POLYNOMIAL MODULES

Zhao, Renyu (College of Economics and Management Northwest Normal University)

Publication Information

Bulletin of the Korean Mathematical Society / v.49, no.5, 2012 , pp. 1067-1079 More about this Journal

Abstract

Let M be a right R-module, (S, ${\leq}$ ) a strictly totally ordered monoid which is also artinian and ${\omega}:S{\rightarrow}Aut(R)$ 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;

Citations & Related Records

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