Prime Submodules of Graded Modules
Let G be a group, R be a G-graded ring and M be a G-graded R-module. Suppose P is a prime ideal of Re and g G G. In this article, we define Mg (P) = {m G Mg : Am C PMg for some ideal A of Re satisfying A C P}that is an Re-submodule of Mg, and we investigate some results on this submodule. Also, we i...
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| Autores principales: | , , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2012
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000400004 |
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| Sumario: | Let G be a group, R be a G-graded ring and M be a G-graded R-module. Suppose P is a prime ideal of Re and g G G. In this article, we define Mg (P) = {m G Mg : Am C PMg for some ideal A of Re satisfying A C P}that is an Re-submodule of Mg, and we investigate some results on this submodule. Also, we introduce a situation where if N is a gr-prime R-submodule of M ,then (Ng : Mg) is a maximal ideal of Re. We close this article by introducing a situation where if N is a gr- R-submodule ofM such that Ne is a weakly prime Re-submodule of Me, then Ng is a prime Re-submodule of Mg. |
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