We define and investigate a sheaf of modules on the prime spectra of modules, and it is shown that there is an isomorphism between the sections of this sheaf and the ideal transform module.

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Let R be a commutative ring with nonzero identity and M be an R-module. Quasi-prime submodules of M and the developed Zariski topology on qSpec(M ) are introduced. We also, investigate the relationship between the algebraic properties of M and the topological properties of qSpec(M ). Modules whose developed Zariski topology is respectively T 0 , irreducible or Noetherian are studied, and several characterizations of such modules are given.

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