Z-primary submodules

Let R is a commutative ring with identity and M be a unitary R -module , a submodule N of an R-module M is called primary if whenever rx E N ; r E R,x E M, then either x E Nor r" 6 [N\ M] for some n 6 Z+. In this paper we say that N is Z -primary submodule of an R -module M if whenever f(x).x E...

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Bibliographic Details
Published in:Iraqi journal of science 2016, Vol.57 (sA), p.163-167
Main Authors: al-Muzaffar, Nihad Salim, Husayn, Ali Talal
Format: Article
Language:ara ; eng
Subjects:
الحلقات
النماذج الرياضية
الوحدات
Online Access:Get full text
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Summary:Let R is a commutative ring with identity and M be a unitary R -module , a submodule N of an R-module M is called primary if whenever rx E N ; r E R,x E M, then either x E Nor r" 6 [N\ M] for some n 6 Z+. In this paper we say that N is Z -primary submodule of an R -module M if whenever f(x).x E N,f E M* = Hom(M,R), xe M, then either x E N or (f(x))n 6 [N:Mf for some n E Z+, where [N: M] = {r: r E R and rM £ N}. We also study a Z-primary module if (0) is a Z-primary submodule of M. We give many properties of Z-primary submodule of M and Z-primary module.
ISSN:0067-2904
2312-1637