Generalized inverse power series modules

摘要

In this article, we introduce a construction called the generalized inverse power series module M[[S~(-1)]] over a monoid ring R[S] with coefficients in an R-module M and exponents in a commutative monoid S. This construction is a generalization of the R[x]-modules which were discussed by S. Park in [12-14]. The injectivity and injective precovers of the generalized inverse power series module are considered. We also show that N is a pure submodule of M if and only if N[S] is a pure submodule of the monoid module M[S].