Locally split submodules and modules with perfect endomorphism rings

G Azumaya - Non-Commutative Ring Theory: Proceedings of a …, 2006 - Springer
Let M be a left module over a ring R. A submodule N of M is called locally split in M if for
each x EN there exists a homomorphism h: Mt N such that h (x)= x. It is shown that if N is …

The singular submodule of a finitely generated module splits off

J Fuelberth, M Teply - Pacific Journal of Mathematics, 1972 - msp.org
A characterization is given of the finitely generated nonsingular left R-modules N such that
Ext R 1 (N, M)= 0 for every singular left R-module M. As a corollary, the rings R, over which …

Chain conditions on direct summands and pure quotient modules

JLG Pardo, PAG Asensio - LECTURE NOTES IN PURE AND …, 2000 - books.google.com
It was shown in [5] that a finitely presented pure-injective module M has an indecomposable
decomposition if and only if M is completely pure-injective, that is, every pure quotient of M is …

Characterization of rings using quasiprojective modules. III

JS Golan - Proceedings of the American Mathematical Society, 1972 - ams.org
A ring $ R $ is regular [completely reducible] if and only if the character module of every left
$ R $-module is quasi-injective [quasiprojective]. Submodules of quasiprojective left $ R …

Prime singular-splitting rings with finiteness conditions

ML Teply - Noncommutative Ring Theory: Papers presented at the …, 2006 - Springer
A module M is said to split if its singular submodule Z (M) is a direct summand of M. If every
R-module splits, R is called a splitting ring. Every splitting ring is a right nonsingular ring. In …

Quasi-projective and quasi-injective modules

A Koehler - Pacific J. Math, 1971 - msp.org
M commutes. The first section of this paper contains results which are needed to prove a
decomposition theorem for quasi-projective modules over left perfect rings (Theorem 1.10) …

[PDF][PDF] On semiperfect and perfect rings

FL Sandomierski - Proceedings of the American Mathematical …, 1969 - community.ams.org
Koh [2] has shown that a commutative ring with identity is semiperfect if and only if every
simple right module has a projective cover. The purpose of this note is to show that the …

[PDF][PDF] Indecomposable decompositions of finitely presented pure-injective modules

JLG Pardo, PAG Asensio - Journal of Algebra, 1997 - core.ac.uk
Ž. It is well known that pure-injective s algebraically compact modules behave well in
relation to direct sum decompositions. Any indecomposable wx pure-injective module has …

[PDF][PDF] Modules which are epi-equivalent to projective modules

GF Birkenmeier - Acta Universitatis Carolinae. Mathematica et Physica, 1983 - dml.cz
The purpose of this paper is to initiate the study of improjective modules. A module X is im-
projective if given any epimorphism/: B-> A and any homomorphism/: X-> A, there exists a …

Indecomposable decompositions of pure-injective modules

N Viet Dung - Communications in Algebra, 1998 - Taylor & Francis
Pureinjective (or algebraically compact) modules have been studied extensively by many
authors (see [lo, 13, 14, 17, 191, for example). One of the main concerns of the theory is the …