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Prime ideals of graded rings and related matters |
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| Authors: | Miguel Ferrero Eric Jespers Edmund R. Puczylowski |
| Affiliation: | 1. Instituto de Matemática , Universidade Federal do Rio Grande do Sul , Porto Alegre, RS, 90049, Brazil;2. Department of Mathematics and Statistics , Memorial University of Newfoundland , St.John's, Newfoundland, A1C5S7, Brazil;3. Department of Mathematics , University of Warsaw , Pkin, Warsaw, 00-901, Poland |
| Abstract: | Let R be a ring graded by an abelian group.We study prime ideals of R that are maximal for not containing nonzero homogeneous elements.Also prime ideals of the symmetric graded Martindale ring of quotients of R are investigated.The results are applied to study when R is a Jacobson ring in case R is a Z-graded ring or a group ring of a finitely generated abelian group, or in case R is right Noetherian and strongly graded by a polycyclic-by-finite group. |
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