scholarly journals ON RICKART MODULES

2019 ◽  
pp. 2473-2477
Author(s):  
Mohammed Qader Rahman ◽  
Bahar Hamad Al-Bahrani
Keyword(s):  
Prime Module ◽  
Rickart Modules

Gangyong Lee, S.Tariq Rizvi, and Cosmin S.Roman studied Rickart modules. The main purpose of this paper is to develop the properties of Rickart modules . We prove that each injective and prime module is a Rickart module. And we give characterizations of some kind of rings in term of Rickart modules.

𝔏-Rickart Modules

2015 ◽  
Vol 43 (5) ◽  
pp. 2124-2151 ◽  
Author(s):  
Gangyong Lee ◽  
S. Tariq Rizvi ◽  
Cosmin S. Roman
Keyword(s):  
Rickart Modules

scholarly journals ON DUAL RICKART MODULES

2020 ◽  
Vol 1530 ◽  
pp. 012038
Author(s):  
Mohammed Qader Rahman ◽  
Bahar hamad Al-Bahram
Keyword(s):  
Rickart Modules

scholarly journals On a class of dual Rickart modules

2020 ◽  
Vol 72 (7) ◽  
pp. 960-970
Author(s):  
R. Tribak
Keyword(s):  
Direct Summand ◽  
Noetherian Ring ◽  
Commutative Noetherian Ring ◽  
Direct Sum ◽  
Finite Set ◽  
Rickart Modules

UDC 512.5 Let R be a ring and let Ω R be the set of maximal right ideals of R . An R -module M is called an sd-Rickart module if for every nonzero endomorphism f of M , ℑ f is a fully invariant direct summand of M . We obtain a characterization for an arbitrary direct sum of sd-Rickart modules to be sd-Rickart. We also obtain a decomposition of an sd-Rickart R -module M , provided R is a commutative noetherian ring and A s s ( M ) ∩ Ω R is a finite set. In addition, we introduce and study ageneralization of sd-Rickart modules.

Dual Rickart Modules

2011 ◽  
Vol 39 (11) ◽  
pp. 4036-4058 ◽  
Author(s):  
Gangyong Lee ◽  
S. Tariq Rizvi ◽  
Cosmin S. Roman
Keyword(s):  
Rickart Modules

Rickart modules relative to singular submodule and dual Goldie torsion theory

2016 ◽  
Vol 15 (08) ◽  
pp. 1650142 ◽  
Author(s):  
Burcu Ungor ◽  
Sait Halicioglu ◽  
Abdullah Harmanci
Keyword(s):  
Torsion Theory ◽  
Arbitrary Ring ◽  
Rickart Modules

Let [Formula: see text] be an arbitrary ring with identity and [Formula: see text] a right [Formula: see text]-module with the ring [Formula: see text] End[Formula: see text] of endomorphisms of [Formula: see text]. The notion of an [Formula: see text]-inverse split module [Formula: see text], where [Formula: see text] is a fully invariant submodule of [Formula: see text], is defined and studied by the present authors. This concept produces Rickart submodules of modules in the sense of Lee, Rizvi and Roman. In this paper, we consider the submodule [Formula: see text] of [Formula: see text] as [Formula: see text] and [Formula: see text], and investigate some properties of [Formula: see text]-inverse split modules and [Formula: see text]-inverse split modules [Formula: see text]. Results are applied to characterize rings [Formula: see text] for which every free (projective) right [Formula: see text]-module [Formula: see text] is [Formula: see text]-inverse split for the preradicals such as [Formula: see text] and [Formula: see text].

Rickart Modules

2010 ◽  
Vol 38 (11) ◽  
pp. 4005-4027 ◽  
Author(s):  
Gangyong Lee ◽  
S. Tariq Rizvi ◽  
Cosmin S. Roman
Keyword(s):  
Rickart Modules

F-CS-RICKART MODULES

2020 ◽  
Vol 45 (1) ◽  
pp. 29-54
Author(s):  
Julalak Kaewwangsakoon ◽  
Sajee Pianskool
Keyword(s):  
Rickart Modules

t-Rickart and Dual t-Rickart Modules

2015 ◽  
Vol 22 (spec01) ◽  
pp. 849-870 ◽  
Author(s):  
Sh. Asgari ◽  
A. Haghany
Keyword(s):  
Direct Summand ◽  
Torsion Module ◽  
Direct Sum ◽  
Rickart Modules ◽  
Baer Modules ◽  
Equivalent Conditions

We introduce the notion of t-Rickart modules as a generalization of t-Baer modules. Dual t-Rickart modules are also defined. Both of these are generalizations of continuous modules. Every direct summand of a t-Rickart (resp., dual t-Rickart) module inherits the property. Some equivalent conditions to being t-Rickart (resp., dual t-Rickart) are given. In particular, we show that a module M is t-Rickart (resp., dual t-Rickart) if and only if M is a direct sum of a Z2-torsion module and a nonsingular Rickart (resp., dual Rickart) module. It is proved that for a ring R, every R-module is dual t-Rickart if and only if R is right t-semisimple, while every R-module is t-Rickart if and only if R is right Σ-t-extending. Other types of rings are characterized by certain classes of t-Rickart (resp., dual t-Rickart) modules.

Prime–Extending Module and S-Prime Module

2011 ◽  
Vol 14 (4) ◽  
pp. 166-170
Author(s):  
Tamadher A. Ibrahiem ◽  
Keyword(s):  
Prime Module ◽  
Extending Module
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