Generalisations of von Neumann regular rings are considered through annihilators, purity
and certain special cyclic modules. Left self-injective regular, strongly regular and biregular …

Throughout this paper, R denotes an associative ring with i, all modules are assumed to be
unital, and J (R) denotes the~ acobson radical of R. If M is a right R-module and S= End M is …

Semiperfect rings, semihereditary rings, and hereditary rings, are characterized by
properties of quasiprojective modules over their matrix rings. In [4], we characterized …

In the second section we shall deal with more general rings than sl: rial rings defined by
Nakayama [lo]. He showed that if a ring R is a serial ring, 1; hen every finitely generated …

On Finitely Generated Modules Over Noetherian Rings Page 1 ON FINITELY GENERATED
MODULES OVER NOETHERIAN RINGS BY JP JANS(Q) 0. Introduction. If A is a module over a …

In an unpublished result dating back to the middle 50's, Kaplansky proved the following:
Kaplansky's Theorem. A commutative ring R is von Neumann regular iff every simple R …

The following conditions are shown to be equivalent: 1) ring A is generalized uniserial (not
necessarily artinian); 2) every finitely presented A module is semiserial; 3) A is semiperfect …

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) …

\S 0. Introduction. The main purpose of this paper is to extend some results on completely
reducible modules to quasi-injective modules by replacing “irreducible submodules” with …

1. Introduction. In [l, pp. 62-63, Exercises 11, 12] Bourbaki in-troduces a generalization of a
left (resp. right) noetherian ring called a left (resp. right) coherent ring and states some …