S-Semiprime Submodules and S-Reduced Modules
| Autor: | Ayten Pekin, Ünsal Tekir, Özge Kılıç |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Journal of Mathematics, Vol 2020 (2020) |
| Druh dokumentu: | article |
| ISSN: | 2314-4629 2314-4785 |
| DOI: | 10.1155/2020/8824787 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|
Plný text