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Öğe On the classical zariski topology over prime spectrum of a module(Jangjeon Research Institute for Mathematical Sciences and Physics, 2017) Qeken S.; Alkan M.Let R be an associative ring with identity and Spec(M) denote the set of all prime submodules of a right R-module M. In this paper, we study the classical Zariski topology on Spec(M) which is denoted by ?c. We prove that if (Spec(M),?c) is a Noetherian topological space, then M has finitely many minimal prime submodules. We characterize all the irreducible components of (Spec(M),rc) and all the minimal prime submodules of M for a non-zero flat module M over a commutative ring R. We obtain some results concerning compactness and connectedness of (Spec(M),?c) by using algebraic properties of the module M. We give some equivalent conditions for (Spec(M),?c) to be a Hausdorff space or T1-space when M is a right module over a left perfect ring R. © 2017 Jangjeon Research Institute for Mathematical Sciences and Physics. All rights reserved.
