Some generalizations of Injectivity
CASC Gomes - 1998 - theses.gla.ac.uk
Chapter 1 covers the background necessary for what follows. In particular, general
properties of injectivity and some of its well-known generalizations are stated. Chapter 2 is …
properties of injectivity and some of its well-known generalizations are stated. Chapter 2 is …
Virtually semisimple modules and a generalization of the Wedderburn-Artin theorem
M Behboodi, A Daneshvar… - Communications in …, 2018 - Taylor & Francis
ABSTRACT A widely used result of Wedderburn and Artin states that “every left ideal of a
ring R is a direct summand of R if and only if R has a unique decomposition as a finite direct …
ring R is a direct summand of R if and only if R has a unique decomposition as a finite direct …
Modules for which every submodule has a unique closure
PF Smith - Ring theory, 1993 - World Scientific
Modules for which every submodule has a unique closure Page 317 302 MODULES FOR
WHICH EVERY SUB MODULE HAS A UNIQUE CLOSURE PATRICK F. SMITH Department of …
WHICH EVERY SUB MODULE HAS A UNIQUE CLOSURE PATRICK F. SMITH Department of …
Nonsingular extending modules
PF Smith - Advances in Ring Theory, 1997 - Springer
NONSINGULAR EXTENDING MODULES Page 1 NONSINGULAR EXTENDING MODULES
PATRICK F. SMITH ABSTRACT. In this paper, it is shown that if R is a semiprime right Goldie …
PATRICK F. SMITH ABSTRACT. In this paper, it is shown that if R is a semiprime right Goldie …
Lifting units in clean rings
J Šter - Journal of Algebra, 2013 - Elsevier
Let R be a clean ring with an ideal I such that R/I is semiperfect and K0 (I) is torsion-free. We
prove that, under some mild conditions, units in R/I can be lifted to units in R. This implies …
prove that, under some mild conditions, units in R/I can be lifted to units in R. This implies …
[PDF][PDF] Essential extensions of a direct sum of simple modules
KI Beidar, SK Jain, AK Srivastava - Contemporary Mathematics, 2006 - researchgate.net
It is known that every essential extension of a direct sum of injective hulls of simple R-
modules is a direct sum of injective R-modules if and only if the ring R is right noetherian …
modules is a direct sum of injective R-modules if and only if the ring R is right noetherian …
▵-Reductions of modules
LJ Ratliff Jr, DE Rush - Communications in Algebra, 1993 - Taylor & Francis
Let△ be a multiplicatively closed set of finitely generated nonzero ideals of a ring R. Then
the concept of a△-reduction of an R-submodule D of an R-module A is introduced and …
the concept of a△-reduction of an R-submodule D of an R-module A is introduced and …
Coneat submodules and coneat-flat modules
E Buyukasik, Y Durgun - Journal of the Korean Mathematical …, 2014 - koreascience.kr
A submodule N of a right R-module M is called coneat if for every simple right R-module S,
any homomorphism $ N {\rightarrow} S $ can be extended to a homomorphism $ M …
any homomorphism $ N {\rightarrow} S $ can be extended to a homomorphism $ M …
Completely coretractable rings
J Zemlicka - Bulletin of the Iranian Mathematical Society, 2013 - bims.iranjournals.ir
A module $ M $ is said to be coretractable if there exists a nonzero homomorphism of every
nonzero factor of $ M $ into $ M $. We prove that all right (left) modules over a ring are …
nonzero factor of $ M $ into $ M $. We prove that all right (left) modules over a ring are …
Weak Relative Injective M-Subgenerated Modules
S Malik, N Vanaja - Advances in Ring Theory, 1997 - Springer
We study weak relative injective and relative tight modules in the category u [M], where M is
a right R-module. Many of the known results in the category of right R-modules are extended …
a right R-module. Many of the known results in the category of right R-modules are extended …