 

Ahmad Yousefian Darani and Mahdi Rahmatinia
On ΦMori modules view print


Published: 
November 27, 2015 
Keywords: 
Mori module; divisorial submodule; ΦMori module, Φdivisorial submodule. 
Subject: 
16D10, 16D80 


Abstract
In this paper we introduce the concept of Mori module. An Rmodule M is said to be a Mori module if it satisfies the ascending chain conditon on divisorial submodules. Then we introduce a new class of modules which is closely related to the class of Mori modules. Let R be a commutative ring with identity and set
H={M  M is an Rmodule and
Nil(M) is a divided prime submodule of M}.
For an Rmodule M∈H, set
T=(R\setminus Z(M))∩ (R\setminus Z(R)),
\mathfrak{T}(M)=T^{1}(M),
P:=[Nil(M):_{R}M].
In this case the mapping Φ:\mathfrak{T}(M)⟶ M_{P} given by Φ(x/s)=x/s is an Rmodule homomorphism. The restriction of Φ to M is also an Rmodule homomorphism from M in to M_{P} given by Φ(m/1)=m/1 for every m∈ M. A nonnil submodule N of M is Φdivisorial if Φ(N) is divisorial submodule of Φ(M). An Rmodule M∈ H is called ΦMori module if it satisfies the ascending chain condition on Φdivisorial submodules. This paper is devoted to study the properties of ΦMori modules.


Author information
Ahmad Yousefian Darani:
Department of Mathematics and Applications, University of Mohaghegh Ardabili, P. O. Box 179, Ardabil, Iran
youseffian@gmail.com
Mahdi Rahmatinia:
Department of Mathematics and Applications, University of Mohaghegh Ardabili, P. O. Box 179, Ardabil, Iran
mahdi.rahmatinia@gmail.com

