Uniform and couniform dimension of generalized inverse polynomial modules
Bull. Korean Math. Soc. 2012 Vol. 49, No. 5, 1067-1079
Printed September 30, 2012
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
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