On rings with associated elements
MT Koşan, TC Quynh, S Şahinkaya - Communications in Algebra, 2017 - Taylor & Francis
ABSTRACT A principal right ideal of a ring is called uniquely generated if any two elements
of the ring that generate the same principal right ideal must be right associated (ie, if for all a …
of the ring that generate the same principal right ideal must be right associated (ie, if for all a …
FPF rings and some conjectures of C. Faith
SS Page - Canadian Mathematical Bulletin, 1983 - cambridge.org
A left FPF ring is a ring R such that every finitely generated faithful left R-module generates
the category of left R-modules. It is shown that such rings split into R= A⊕ B, where A is a …
the category of left R-modules. It is shown that such rings split into R= A⊕ B, where A is a …
On some characteristic properties of self-injective rings
K Koh - Proceedings of the American Mathematical Society, 1968 - JSTOR
F= R ED R ED** ED R (n copies) for some positive integer n and let M be a cyclic submodule
of F. Then M= Rmo for some mO EF and mo= a1+ a2+***+ a. for some ai, a2,**, an in R. Let …
of F. Then M= Rmo for some mO EF and mo= a1+ a2+***+ a. for some ai, a2,**, an in R. Let …
When cyclic modules have Σ-injective hulls
C Faith - Communications in Algebra, 2003 - Taylor & Francis
A theorem of Cartan-Eilenberg (Cartan, H., Eilenberg, S.(1956). Homological Algebra.
Princeton: Princeton University Press, pp. 390.) states that a ring R is right Noetherian iff …
Princeton: Princeton University Press, pp. 390.) states that a ring R is right Noetherian iff …
[HTML][HTML] Simple-direct-injective modules
A module M over a ring is called simple-direct-injective if, whenever A and B are simple
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …
When is a simple ring Noetherian?
D Van Huynh, SK Jain, SR López-Permouth - Journal of algebra, 1996 - Elsevier
A moduleMis known to be a CS-module (or an extending module) if every complement
submodule ofMis a direct summand. It is shown that (i) a simple ringRmust be right …
submodule ofMis a direct summand. It is shown that (i) a simple ringRmust be right …
Simple self-injective rings need not be Artinian
KR Goodearl - Communications in Algebra, 1974 - Taylor & Francis
The purpose of this note is to provide examples of simple, right and left self-injective rings
which are not artinian, thus contradicting a theorem of S. Elliger [“On simple injective rings” …
which are not artinian, thus contradicting a theorem of S. Elliger [“On simple injective rings” …
π-injective modules and rings whose cyclics are π-injective
VK Goel, SK Jain - Communications in Algebra, 1978 - Taylor & Francis
6 0 GOEL AND JAIN self-injective ring (or if R is a semiperfect ring) then each cyclic R-
module is a-injective if and only if R is a direct sum of semisimple artinian ring and a finite …
module is a-injective if and only if R is a direct sum of semisimple artinian ring and a finite …
Extending modules which are direct sums of injective modules and semisimple modules
C Santa-Clara, PF Smith - Communications in Algebra, 1996 - Taylor & Francis
Extending modules which are direct sums of injective modules and semisimple modules Page 1
COMMUNICATIONS IN ALGEBRA, 24(1 I), 3641-3651 (1996) Extending modules which are …
COMMUNICATIONS IN ALGEBRA, 24(1 I), 3641-3651 (1996) Extending modules which are …