A Sheaf On The Second Spectrum Of A Module

Abstract: Let R be a commutative ring with identity and Specs(M) denote the set all second submodules of an R-module M. In this paper, we construct and study a sheaf of modules, denoted by O(N; M), on Specs(M) equipped with the dual Zariski topology of M, where N is an R-module. We give a characterization of the sections of the sheaf O(N; M) in terms of the ideal transform module. We present some interrelations between algebraic properties of N and the sections of O(N; M). We obtain some morphisms of sheaves induced by ring and module homomorphisms.