scholarly journals On dual $\pi$-endo Baer modules

2021 ◽  
Vol 9 (2) ◽  
pp. 39-45
Author(s):  
Yeliz Kara
Keyword(s):  
Baer Modules

scholarly journals Baer-Galois connections and applications

2014 ◽  
Vol 30 (2) ◽  
pp. 225-229
Author(s):  
GABRIELA OLTEANU ◽  
Keyword(s):  
Modular Lattices ◽  
Galois Connections ◽  
Baer Modules

We define Baer-Galois connections between bounded modular lattices. We relate them to lifting lattices and we show that they unify the theories of (relatively) Baer and dual Baer modules.

t-Extending Modules andt-Baer Modules

2011 ◽  
Vol 39 (5) ◽  
pp. 1605-1623 ◽  
Author(s):  
Sh. Asgari ◽  
A. Haghany
Keyword(s):  
Baer 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.

scholarly journals Direct sums of quasi-Baer modules

2016 ◽  
Vol 456 ◽  
pp. 76-92 ◽  
Author(s):  
Gangyong Lee ◽  
S. Tariq Rizvi
Keyword(s):  
Direct Sums ◽  
Baer Modules

On Dual Baer Modules

2014 ◽  
pp. 173-184 ◽  
Author(s):  
Derya Keskin Tütüncü ◽  
Patrick Smith ◽  
Sultan Toksoy
Keyword(s):  
Baer Modules

scholarly journals WEAK and CO-WEAK BAER MODULES: موديلات بيير الضعيفة والضعيفة المرافقة

2021 ◽  
Vol 5 (4) ◽  
pp. 110-98
Author(s):  
Eaman Al-Khouja, Magd Alfakhory, Hamza Hakmi Eaman Al-Khouja, Magd Alfakhory, Hamza Hakmi
Keyword(s):  
Endomorphism Ring ◽  
Free Module ◽  
Orthogonal Idempotent ◽  
Baer Modules ◽  
Infinite Set

The object of this paper is study the notions of weak Baer and weak Rickart rings and modules. We obtained many characterizations of weak Rickart rings and provide their properties. Relations ship between a weak Rickart (weak Baer) module and its endomorphism ring are studied. We proved that a weak Baer module with no infinite set of nonzero orthogonal idempotent elements in its endomorphism ring is precisely a Baer module. In addition, the endomorphism ring of a semi-projective weak Rickart module is semi-potent and the endomorphism ring of a semi-injective coweak Rickart module is semi-potent. Furthermore, we show that a free module is weak Baer if and only if its endomorphism ring is left weak Baer.

scholarly journals Baer and Quasi-Baer Modules

2004 ◽  
Vol 32 (1) ◽  
pp. 103-123 ◽  
Author(s):  
S. Tariq Rizvi ◽  
Cosmin S. Roman
Keyword(s):  
Baer Modules

Endo-principally quasi-Baer modules

2015 ◽  
Vol 15 (02) ◽  
pp. 1550132 ◽  
Author(s):  
P. Amirzadeh Dana ◽  
A. Moussavi
Keyword(s):  
Direct Summand ◽  
Endomorphism Ring ◽  
Free Module ◽  
Baer Ring ◽  
Baer Rings ◽  
Baer Modules

Analogous to left p.q.-Baer property of a ring [G. F. Birkenmeier, J. Y. Kim and J. K. Park, Principally quasi-Baer rings, Comm. Algebra29 (2001) 639–660], we say a right R-module M is endo-principallyquasi-Baer (or simply, endo-p.q.-Baer) if for every m ∈ M, lS(Sm) = Se for some e2 = e ∈ S = End R(M). It is shown that every direct summand of an endo-p.q.-Baer module inherits the property that any projective (free) module over a left p.q.-Baer ring is an endo-p.q.-Baer module. In particular, the endomorphism ring of every infinitely generated free right R-module is a left (or right) p.q.-Baer ring if and only if R is quasi-Baer. Furthermore, every principally right ℱℐ-extending right ℱℐ-𝒦-nonsingular ring is left p.q.-Baer and every left p.q.-Baer right ℱℐ-𝒦-cononsingular ring is principally right ℱℐ-extending.

scholarly journals On direct sums of Baer modules

2009 ◽  
Vol 321 (2) ◽  
pp. 682-696 ◽  
Author(s):  
S. Tariq Rizvi ◽  
Cosmin S. Roman
Keyword(s):  
Direct Sums ◽  
Baer Modules
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