44 - M. Behboodi (Joint with M. Aghasi and M. Zabzevari) A Structure Sheaf on the Spectrum of Prime Radical Modules, Journal of Commutative Algebra (Accepted) (ISI)
We study modules satisfying the prime radical condition, which are called P-radical modules, in the point of algebraic geometry view. This study shows that the theory of spectrum of these modules, equipped with the Zariski topology,resembles to that of commutative rings with identity. First, we investigate the behavior of P-radical modules under localization and direct sums. Then for an R-module M, we describe the construction of a structure sheaf on the prime spectrum Spec(M), which generalizes the classical structure sheaf of the ring R in Algebraic Geometry to the R-module M.