Prime Submodules of Graded Modules

Abu-Dawwas, Rashid ^[1] ; Al-Zoubi, Khaldoun ^[2] ; Bataineh, Malik ^[2]
1. [1] Yarmouk University
  
  Yarmouk University
  
  Jordania
2. [2] Jordan University of Science and Technology
  
  Jordan University of Science and Technology
  
  Jordania
Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 31, Nº. 4, 2012, págs. 355-361
Idioma: inglés
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Resumen
- 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 Reand g G G. In this article, we defineMg (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 ofMe,thenNg is a prime Re-submodule of Mg.