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 …

1. Introduction. Let R be a ring with identity. A right i?-module M is said to be¿(i? Ä)-
torsionless, if M is isomorphic to a submodule of a direct product o E {Rr), where E (Rr) is the …

We study modules M such that all automorphisms of submodules in M can be extended to
endomorphisms (automorphisms) of M. All rings are assumed to be associative and with …

In 1-4] Nakayama proved that every module M over a generalized uniserial ring has a
decomposition M=~) M~ in which each term is A uniserial (ie, its submodules form a chain) …

788 INJECTIVE MODULES UNDER CHANGE OF RINGS1 Page 1 788 ERNST SNAPPER [August
Bibliography 1. L. Auslander and M. Kuranishi, On the holonomy group of locally Euclidean …

In [3] C. Faith and EA Walker gave a characterization of a left artinian ring in terms of module
theories. That is, a ring B is left artinian if and only if every injective left B-module is a direct …

In [3], it is shown that a ring P such that every cyclic right P-module is injective must be
semisimple Artin. In this note, that proof is greatly simplified, and it is shown that a hereditary …

This is of course equivalent to the condition that every simple module is either projective or
injective. Theorem 1.1 gives necessary and sufficient conditions for a T-ring to have property …

Let RP be a projective R-module which is not finitely generated. Let E= End R (P). This
paper examines the structure of P as an E-module and relations between right ideals of R …