Group graded types of Bezout modules
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In this paper, we introduce two group graded types of B\'ezout modules, namely graded-B\'ezout modules and weakly graded-B\'ezout modules, which are two B\'ezout versions in Graded Module Theory. We investigate the relationship among the three types of B\'ezout modules, the ordinary B\'ezout modules and the two graded types of B\'ezout modules. Also, we study the structure of these new B\'ezout modules along with different properties; for instance, ``A graded-B\'ezout $R$-module, with $R$ being a Noetherian ring, is Noetherien iff it is $gr$-Noetherian".
Abstract
In this paper, we introduce two group graded types of B\'ezout modules, namely graded-B\'ezout modules and weakly graded-B\'ezout modules, which are two B\'ezout versions in Graded Module Theory. We investigate the relationship among the three types of B\'ezout modules, the ordinary B\'ezout modules and the two graded types of B\'ezout modules. Also, we study the structure of these new B\'ezout modules along with different properties; for instance, ``A graded-B\'ezout $R$-module, with $R$ being a Noetherian ring, is Noetherien iff it is $gr$-Noetherian".
참고문헌 (6)
- M. Boulagouaz, "Algebra and Number Theory" (1999), CRC Press
- A. Khaksari, "Multiplication graded modules", Int. J. Algebra, 7(1), pp.17~24 (2013)
- C. Nastasescu, "Graded Ring Theory", Mathematical library, 28 (1982), North Holand
- M. Refai, "On Flexible graded modules", Ital. J. Pure Appl. Math, 22, pp.125~132 (2007)
- A. Tuganbaev, "Rings Close to Regular" (2013), Springer Science and Business Media
- A. Vasil’evich Mikhalev, "The Concise Handbook of Algebra" (2002), Springer Science and Business Media