Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2017; 32(3): 523-534

Online first article June 9, 2017      Printed July 31, 2017

https://doi.org/10.4134/CKMS.c160199

Copyright © The Korean Mathematical Society.

Group graded types of B\'ezout modules

Mamoon Ahmed and Fida Moh'D

Princess Sumaya University for Technology, Princess Sumaya University for Technology

Abstract

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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".

Keywords: graded rings, graded modules, B\'ezout modules, graded B\'ezout modules, weakly graded B\'ezout modules

MSC numbers: 13A02

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