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 …

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 …

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 …

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 …

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 …

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) …

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 …

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 …

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 …

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 …