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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".
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M. Boulagouaz / 1999 / Algebra and Number Theory / CRC Press
A. Khaksari / 2013 / Multiplication graded modules / Int. J. Algebra 7(1):17~24
C. Nastasescu / 1982 / Graded Ring Theory / Mathematical library 28
M. Refai / 2007 / On Flexible graded modules / Ital. J. Pure Appl. Math 22:125~132
A. Tuganbaev / 2013 / Rings Close to Regular / Springer Science and Business Media
A. Khaksari / 2013 / Multiplication graded modules / Int. J. Algebra 7(1):17~24
C. Nastasescu / 1982 / Graded Ring Theory / Mathematical library 28
M. Refai / 2007 / On Flexible graded modules / Ital. J. Pure Appl. Math 22:125~132
A. Tuganbaev / 2013 / Rings Close to Regular / Springer Science and Business Media
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