[图书][B] Extending modules
NV Dung - 2019 - taylorfrancis.com
Module theory is an important tool for many different branches of mathematics, as well as
being an interesting subject in its own right. Within module theory, the concept of injective …
being an interesting subject in its own right. Within module theory, the concept of injective …
[图书][B] Lifting modules: supplements and projectivity in module theory
Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …
generalize projective supplemented modules. There is a certain asymmetry in this duality …
[引用][C] Quasi-Frobenius Rings
WK Nicholson - Cambridge Tracts in Math/Cambridge University …, 2003 - books.google.com
A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all
four combinations are equivalent). The study of these rings grew out of the theory of …
four combinations are equivalent). The study of these rings grew out of the theory of …
Goldie extending modules
E Akalan, GF Birkenmeier, A Tercan - Communications in Algebra, 2009 - Taylor & Francis
In this article, we define a module M to be 𝒢-extending if and only if for each X≤ M there
exists a direct summand D of M such that X∩ D is essential in both X and D. We consider …
exists a direct summand D of M such that X∩ D is essential in both X and D. We consider …
[PDF][PDF] Extending modules over commutative domains
MA Kamal, BJ Müller - 1988 - projecteuclid.org
A module is extending (or has the property (Q)) if every complement submodule is a direct
summand. We prove that a module over a commutative domain has this property, if and only …
summand. We prove that a module over a commutative domain has this property, if and only …
On almost M-projectives and almost M-injectives
Y Baba, M Harada - Tsukuba journal of mathematics, 1990 - JSTOR
We have defined aconcept of almost M-projectives and almost M-injectives in [4] and [9],
respectively. In the first section of this paper we give some relations among lifting modules …
respectively. In the first section of this paper we give some relations among lifting modules …
[PDF][PDF] Finite direct sums of CS-modules
A Harmanci, PF Smith - Houston J. Math, 1993 - Citeseer
Let R be a ring and let M= M•© M2 be a right R-module which is the direct sum of
submodules M•, M2. We are interested in conditions on M•, M2 which make M a CS-module …
submodules M•, M2. We are interested in conditions on M•, M2 which make M a CS-module …
CS-modules and weak CS-modules
PF Smith - Non-Commutative Ring Theory: Proceedings of a …, 2006 - Springer
Weak as-modules share some of the properties of as-modules. For example, we prove that if
M is a weak CS-module which satisfies the ascending chain condition on essential …
M is a weak CS-module which satisfies the ascending chain condition on essential …
Ojective modules
SH Mohamed, BJ Müller - 2002 - Taylor & Francis
A module is extending (or a CS-module, or a module with if every submodule is essential in
a direct summand (equivalen tly, if every closed submodule is a direct summand). Extending …
a direct summand (equivalen tly, if every closed submodule is a direct summand). Extending …