The study of Properties of Reduced Modules

یوسفیان دارانی, احمد (2018) The study of Properties of Reduced Modules. University of Mohaghegh Ardabili, University of Mohaghegh Ardabili.

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Abstract

We introduce reduced modules over a commutative ring and z0-submodules. Let R be a commutative ring and M an R-module. An R-module M is called reduced if M has no nonzero nilpotent elements. A proper submodule N of M is called a z0-submodule if for each m 2 N, the intersection of all minimal prime submodules of M containing m is contained in N. We denote by h(S), for S � M, the set of all minimal prime submodules of M containing S. IfM is a faithful multiplication reduced R-module, then a prime submodule N of M is minimal if and only if for any m 2 N there exists r 2 R n (N :R M) such that rm = 0. Also, for S � M, annR(S)M = ∩ Q, where Q 2 Min(M) n h(S). Moreover, if N is a nilpotent z0-submodule of M, then every prime submodule of M, minimal over N is a prime z0-submodule and N is equal to an intersection of prime z0-submodules. We introduce property A onM and show that, if the R-moduleM satisfies property A, then any submodule N of M is contained in a z0-submodule.

Item Type: Other
Persian Title: The study of Properties of Reduced Modules
Persian Abstract: -
Subjects: Research Projects
Divisions: Subjects > Faculty of Basic Sciences > Department of Mathematics
Faculty of Basic Sciences > Department of Mathematics
Date Deposited: 14 Jul 2019 04:48
Last Modified: 14 Jul 2019 04:48
URI: http://repository.uma.ac.ir/id/eprint/8393

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