π-endo Baer modules

2019 ◽  
Vol 48 (3) ◽  
pp. 1132-1149
Author(s):  
Gary F. Birkenmeier ◽  
Yeliz Kara ◽  
Adnan Tercan
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 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

scholarly journals Weak baer modules localized with respect to a torsion theory

1998 ◽  
Vol 48 (1) ◽  
pp. 173-176
Author(s):  
Seog-Hoon Rim ◽  
Mark L. Teply
Keyword(s):  
Torsion Theory ◽  
Baer Modules
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