A Class of Retractable and Coretractable Modules

2022 ◽  
Author(s):  
Najia Merrachi ◽  
Rachid Tribak
Keyword(s):  
Coretractable Modules

scholarly journals Weakly Coretractable Modules

2018 ◽  
Vol 1003 ◽  
pp. 012061 ◽  
Author(s):  
Inaam M A Hadi ◽  
Shukur N Al-aeashi
Keyword(s):  
Coretractable Modules

scholarly journals ESSENTIAL AND RETRACTABLE GALOIS CONNECTIONS

2013 ◽  
Vol 12 (06) ◽  
pp. 1350017 ◽  
Author(s):  
SEPTIMIU CRIVEI
Keyword(s):  
Bijective Correspondence ◽  
Galois Connections ◽  
Injective Modules ◽  
Uniform Dimension ◽  
Coretractable Modules

For bounded lattices, we introduce certain Galois connections, called (cyclically) essential, retractable and UC Galois connections, which behave well with respect to concepts of module-theoretic nature involving essentiality. We show that essential retractable Galois connections preserve uniform dimension, whereas essential retractable UC Galois connections induce a bijective correspondence between sets of closed elements. Our results are applied to suitable Galois connections between submodule lattices. Cyclically essential Galois connections unify semi-projective and semi-injective modules, while retractable Galois connections unify retractable and coretractable modules.

scholarly journals S-T-CORETRACTABLE MODULES

2021 ◽  
Vol 52 (1) ◽  
pp. 1-15
Author(s):  
Mouhamadou Lamine Dia ◽  
Papa Cheikhou Diop ◽  
Abdoul Djibril Diallo ◽  
Mamadou Barry
Keyword(s):  
Coretractable Modules

scholarly journals On coretractable modules

2015 ◽  
Vol 44 (1) ◽  
pp. 91-99 ◽  
Author(s):  
Derya KESKİN TÜTÜNCÜ ◽  
Berke KALEBO~GAZ
Keyword(s):  
Coretractable Modules

scholarly journals CORETRACTABLE MODULES

2009 ◽  
Vol 86 (3) ◽  
pp. 289-304 ◽  
Author(s):  
B. AMINI ◽  
M. ERSHAD ◽  
H. SHARIF
Keyword(s):  
Commutative Rings ◽  
Endomorphism Rings ◽  
Perfect Ring ◽  
Coretractable Modules

AbstractAn R-module M is called coretractable if  HomR(M/K,M)≠0 for any proper submodule K of M. In this paper we study coretractable modules and their endomorphism rings. It turns out that if all right R-modules are coretractable, then R is a right Kasch and (two-sided) perfect ring. However, the converse holds for commutative rings. Also, for a semi-injective coretractable module MR with S=EndR(M), we show that u.dim(SS)=corank(MR).

Retractable and Coretractable Modules

2016 ◽  
Vol 213 (2) ◽  
pp. 132-142 ◽  
Author(s):  
A. N. Abyzov ◽  
A. A. Tuganbaev
Keyword(s):  
Coretractable Modules

scholarly journals P-Coretractable and Strongly P-Coretractable Modules

2017 ◽  
Vol 5 (2) ◽  
Author(s):  
Inaam Mohammed Ali Hadi ◽  
Shukur Neamah Al-aeashi
Keyword(s):  
Basic Properties ◽  
Coretractable Modules

In this paper, we introduce the notion of P-coretractable module . Some basic properties of this class of modules are investigated and some relationships between these modules and other related concepts are introduced . Also , we give the notion of strongly P-coretractable and study it comparison with P-coretractable , moreover the mono-P-coretractable concept are introduced and studied .

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