On direct sums of Baer modules
ST Rizvi, CS Roman - Journal of Algebra, 2009 - Elsevier
The notion of Baer modules was defined recently. Since a direct sum of Baer modules is not
a Baer module in general, an open question is to find necessary and sufficient conditions for …
a Baer module in general, an open question is to find necessary and sufficient conditions for …
On 𝒦-nonsingular modules and applications
ST Rizvi, CS Roman - Communications in Algebra, 2007 - Taylor & Francis
We introduce the notion of 𝒦-nonsingularity of a module and show that the class of 𝒦-
nonsingular modules properly contains the classes of nonsingular modules and of polyform …
nonsingular modules properly contains the classes of nonsingular modules and of polyform …
[PDF][PDF] Small monoform modules
MA Inaam, HK Marhun - Ibn AL-Haitham journal for pure and applied …, 2017 - iasj.net
Let R be a commutative ring with unity, let M be a left R-module. In this paper we introduce
the concept small monoform module as a generalization of monoform module. A module M …
the concept small monoform module as a generalization of monoform module. A module M …
On closed Rickart modules
MA Kareem, IM Ali - Iraqi Journal of science, 2016 - ijs.uobaghdad.edu.iq
In this article, we study the notion of closed Rickart modules. A right R-module M is said to
be closed Rickart if, for each, is a closed submodule of M. Closed Rickart modules is a …
be closed Rickart if, for each, is a closed submodule of M. Closed Rickart modules is a …
[PDF][PDF] Strongly Rickart Modules
SA Al-Saadi, TA Ibrahiem - Journal of advances in mathematics, 2014 - core.ac.uk
In this paper we introduce and study the concept of strongly Rickart modules and strongly
CS-Rickart modules as a stronger than of Rickart modules [8] and CS-Rickart modules [3] …
CS-Rickart modules as a stronger than of Rickart modules [8] and CS-Rickart modules [3] …
Principally quasi-Baer skew power series modules
A module MR is called principally quasi-Baer (or simply pq-Baer) if the annihilator of every
cyclic submodule of MR is generated by an idempotent, as a right ideal. Let α be an …
cyclic submodule of MR is generated by an idempotent, as a right ideal. Let α be an …
Transfer of certain properties from modules to their endomorphism rings
G Lee, ST Rizvi, CS Roman - Contemporary Mathematics, 2014 - books.google.com
The study of the endomorphism rings of modules and connections between a module and its
endomorphism ring have long been of interest. Of particular interest has been a quest of …
endomorphism ring have long been of interest. Of particular interest has been a quest of …
When do the direct sums of modules inherit certain properties?
G Lee, S TARIQ RIZVI, C Roman - Contemporary Ring Theory 2011, 2012 - World Scientific
It is of obvious interest to know whether an algebraic property of modules is preserved by
direct sums of such modules. In this paper we provide a survey of this question for various …
direct sums of such modules. In this paper we provide a survey of this question for various …
[PDF][PDF] Strongly Essential Submodules and Modules with the se-CIP
TY Ghawi - Iraqi Journal of Science, 2023 - iasj.net
Let 𝑅 be a ring with identity. Recall that a submodule 𝑁 of a left 𝑅-module 𝑀 is called
strongly essential if for any nonzero subset 𝑋 of 𝑀, there is 𝑟∈ 𝑅 such that (0≠) 𝑟𝑋⊆ 𝑁 …
strongly essential if for any nonzero subset 𝑋 of 𝑀, there is 𝑟∈ 𝑅 such that (0≠) 𝑟𝑋⊆ 𝑁 …