UNIFORM AND COUNIFORM DIMENSION OF GENERALIZED INVERSE POLYNOMIAL MODULES

Let M be a right R-module, (S, <=) a strictly totally ordered monoid which is also artinian and omega : S -> Aut(R) a monoid homomorphism, and let [M-S,M-<=]([[RS,<=,omega]]) denote the generalized inverse polynomial module over the skew generalized power series ring [[R-S,R-<=, omega]]. In this paper, we prove that [M-S,M-<=]([[RS,<=,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,M-<=]([[RS,<=,omega]]) has the same couniform dimension as its coefficient module M-R.