UNIFORM AND COUNIFORM DIMENSION OF GENERALIZED INVERSE POLYNOMIAL MODULES

Title & Authors
UNIFORM AND COUNIFORM DIMENSION OF GENERALIZED INVERSE POLYNOMIAL MODULES
Zhao, Renyu;

Abstract
Let M be a right R-module, (S, $\small{{\leq}}$) a strictly totally ordered monoid which is also artinian and $\small{{\omega}:S{\rightarrow}Aut(R)}$ a monoid homomorphism, and let $\small{[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]}$ denote the generalized inverse polynomial module over the skew generalized power series ring [[$\small{R^{S,{\leq}},{\omega}}$]]. In this paper, we prove that $\small{[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]}$ has the same uniform dimension as its coefficient module $\small{M_R}$, and that if, in addition, R is a right perfect ring and S is a chain monoid, then $\small{[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]}$ has the same couniform dimension as its coefficient module $\small{M_R}$.
Keywords
skew generalized power series ring;generalized inverse polynomial module;uniform dimension;couniform dimension;
Language
English
Cited by
1.
Attached prime ideals of generalized inverse polynomial modules, Asian-European Journal of Mathematics, 2017, 10, 02, 1750023
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