S-Semiprime Submodules and S-Reduced Modules
This article introduces the concept of S-semiprime submodules which are a generalization of semiprime submodules and S-prime submodules. Let M be a nonzero unital R-module, where R is a commutative ring with a nonzero identity. Suppose that S is a multiplicatively closed subset of R. A submodule P o...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8824787 |
| Summary: | This article introduces the concept of S-semiprime submodules which are a generalization of semiprime submodules and S-prime submodules. Let M be a nonzero unital R-module, where R is a commutative ring with a nonzero identity. Suppose that S is a multiplicatively closed subset of R. A submodule P of M is said to be an S-semiprime submodule if there exists a fixed s∈S, and whenever rnm∈P for some r∈R,m∈M, and n∈ℕ, then srm∈P. Also, M is said to be an S-reduced module if there exists (fixed) s∈S, and whenever rnm=0 for some r∈R,m∈M, and n∈ℕ, then srm=0. In addition, to give many examples and characterizations of S-semiprime submodules and S-reduced modules, we characterize a certain class of semiprime submodules and reduced modules in terms of these concepts. |
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| ISSN: | 2314-4629 2314-4785 |