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- W2068673532 abstract "Let R be an associative ring with identity and Spec s (M) denote the set of all second submodules of a right R-module M. In this paper, we investigate some interrelations between algebraic properties of a module M and topological properties of the second classical Zariski topology on Spec s (M). We prove that a right R-module M has only a finite number of maximal second submodules if and only if Spec s (M) is a finite union of irreducible closed subsets. We obtain some interrelations between compactness of the second classical Zariski topology of a module M and finiteness of the set of minimal submodules of M. We give a connection between connectedness of Spec s (M) and decomposition of M for a right R-module M. We give several characterizations of a noetherian module M over a ring R such that every right primitive factor of R is artinian for which Spec s (M) is connected." @default.
- W2068673532 created "2016-06-24" @default.
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- W2068673532 date "2015-09-01" @default.
- W2068673532 modified "2023-10-15" @default.
- W2068673532 title "On the second spectrum and the second classical Zariski topology of a module" @default.
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- W2068673532 doi "https://doi.org/10.1142/s0219498815501509" @default.
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