A SCHEME OVER QUASI-PRIME SPECTRUM OF MODULES

The notions of quasi-prime submodules and developed Zariski topology was introduced by the present authors in [1]. In this paper we use these notions to define a scheme. For an R- module M, let X := {Q ? qSpec(M) | (Q :R M) ? Spec(R)}. It is proved that (X,OX) is a locally ringed space. We study the morphism of locally ringed spaces induced by R-homomorphism M ? N, and also by ring homomorphism R ? S. Among other results, we show that (X,OX) is a scheme by putting some suitable conditions on M.