2. Let A be a simple algebra over a field F-GF [2]. In order that the results obtained here will
be valid also for simple rings which do not contain a unit, we extend the meaning of" inner …

A commutative ring with unit is called a d-ring if every finitely generated Loewy module is a
direct sum of cyclic submodules. It is shown that every d-ring is a T-ring, ie, Loewy modules …

We prove that for a ring $ R $, the following are equivalent:(i) Every right $ R $-module is a
direct sum of extending modules, and (ii) $ R $ has finite type and right colocal type (ie …

Throughout R will represent a ring with unit element 1, and all modules will be unitary 7?-
modules. We call a module M a completely indecomposable module if the endomorphism …

1. TRELIMI~ JA3ICS STANDARD MODULES. Throughout% is paper R is an artinian rir. 5:~
itk radical J= J (R). For the nost? art we shall dsal with lef', 3-m. odules.'t; e write cc 15: for the …

SOME MODEL THEORY OVER AN EXCEPTIONAL UNISERIAL RING AND DECOMPOSITIONS
OF SERIAL MODULES Page 1 J. London Math. Soc. (2) 64 (2001) 311–326 Cf2001 London …

Theorem (K6the-Cohen-Kaplansky). A commutative ring R has the property that each of its R-
modules is a direct sum of cyclic modules if and only if R is an artinian principal ideal ring …

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 …

We shall extend those relations to more general rings. In the second section we shall study
ringsR with the lifting (extending) property of simple modules as right i?-modules by making …

The main theorem of this paper names seven ring classifications which coincide with the
class of rings named in the title. Three of them are (1) rings over which every module is …