Some new results on regular modules
The aim of this paper is to study unitary regular modules on commutative rings with identity.
Regularity accompanied by cocyclic property results in some prime-related conclusions on …
Regularity accompanied by cocyclic property results in some prime-related conclusions on …
On regular modules over commutative rings
D Hassanzadeh-Lelekaami… - Bulletin of the Malaysian …, 2019 - Springer
In this paper, we investigate the class of von Neumann regular modules over commutative
rings. More precisely, we introduce a characterization of regular modules, and then, we …
rings. More precisely, we introduce a characterization of regular modules, and then, we …
Prime submodules of regular modules over commutative rings
M Ershad, N Amiri - Arabian Journal for Science and Engineering, 2011 - Springer
We investigate prime submodules of regular modules. In particular, we shall see that every
proper submodule of a regular module M over an integral domain is prime. Although (von …
proper submodule of a regular module M over an integral domain is prime. Although (von …
Submodules of secondary modules
SE Atani - … Journal of Mathematics and Mathematical Sciences, 2002 - Wiley Online Library
Let R be a commutative ring with nonzero identity. Our objective is to investigate
representable modules and to examine in particular when submodules of such modules are …
representable modules and to examine in particular when submodules of such modules are …
[PDF][PDF] Characterizations of regular modules
PI Kimuli, D Ssevviiri - International Electronic Journal of Algebra, 2023 - dergipark.org.tr
Different and distinct notions of regularity for modules exist in the literature. When these
notions are restricted to commutative rings, they all coincide with the well-known von …
notions are restricted to commutative rings, they all coincide with the well-known von …
-regular modules
GN Sudharshana, D Sivakumar - Missouri Journal of Mathematical …, 2023 - projecteuclid.org
The notion of $ R $-regular module is introduced. We will show that if $ M $ is a torsion-free
module over a commutative ring, then $ M $ is $ R $-regular module if and only if $ M $ is a …
module over a commutative ring, then $ M $ is $ R $-regular module if and only if $ M $ is a …
On weakly prime submodules
SE Atani, F Farzalipour - Tamkang Journal of Mathematics, 2007 - journals.math.tku.edu.tw
Let $ R $ be a commutative ring with non-zero identity. We define a proper submodule $ N $
of an $ R $-module $ M $ to be weakly prime if $0\not= rm\in N $($ r\in R, m\in M $) implies …
of an $ R $-module $ M $ to be weakly prime if $0\not= rm\in N $($ r\in R, m\in M $) implies …
[PDF][PDF] On regularity of rings
JL Chen, NQ Ding - Algebra Colloquium, 2001 - maths.nju.edu.cn
ON REGULARITY OF RINGS 1 Page 1 ON REGULARITY OF RINGS 1 Jianlong Chen Department
of Mathematics, Harbin Institute of Technology Harbin 150001, PR China and Department of …
of Mathematics, Harbin Institute of Technology Harbin 150001, PR China and Department of …
On property (𝒜) for modules over direct products of rings
S Bouchiba, M El-Arabi - Quaestiones Mathematicae, 2021 - Taylor & Francis
In this paper we show that if {Ri} i∈ I is a family of commutative rings and {Mi} i∈ I is a family
of modules such that each Mi is an Ri-module, then the direct product Mi is a-module over Ri …
of modules such that each Mi is an Ri-module, then the direct product Mi is a-module over Ri …
[引用][C] On weakly prime submodules
F Farzalipour - Tamkang Journal of Mathematics, 2007 - airitilibrary.com
Let R be a commutative ring with non-zero identity. We define a proper submodule N of an R-
module M to be weakly prime if 0≠ rm∈ N (r∈ R, m∈ M) implies m∈ N or rM⊆ N. A …
module M to be weakly prime if 0≠ rm∈ N (r∈ R, m∈ M) implies m∈ N or rM⊆ N. A …