INJECTIVE PRECOVERS AND MODULES OF GENERALIZED INVERSE POLYNOMIALS.

This paper is motivated by S. Park [10] in which the injective cover of left R[x]-module M[x[sup -1]] of inverse polynomials over a left R-module M was discussed. The author considers the Ω-covers of modules and shows that if η: P → M is an Ω-cover of M, then [η[sup S,≤]] : [P[sup S,≤]] → [M[sup S,≤]] is an [Ω[sup S,≤]]-cover of left [[R[sup S,≤]]]-module [M[sup S,≤]], where Ω is a class of left R-modules and [M[sup S,≤]] is the left [[R[sup S,≤]]]-module of generalized inverse polynomials over a left R-module M. Also some properties of the injective cover of left [[R[sup S,≤]]]-module [M[sup S,≤]] are discussed. [ABSTRACT FROM AUTHOR]