… the longstanding conjectures in ring theory. Although it … rings under certain conditions. The
purpose of this article is to obtain extensions of such results over CohenMacaulay local rings …

… a ring R right self FPinjective if it has the property that it is pure, as a right jR-module, in every
ring extension? … Rings which are pure in all ring extensions were studied by Sabbagh in [4] …

… local rings could be subsumed under the study of injective modules E over a commutative
ring A … over any ring, and hence the study of Morita self-dualities, is contained in the study of …

… Throughout this note, all rings will be self-basic connected artin algebras over a fixed
commutative local artin ring k and all modules will be finitely generated. Homomorphisms will be …

In this paper we generalize to dimensions greater than one a theorem of Greenberg [9], and
we apply this generalization to some algebraization problems. Some of our results are …

… extensions of several results cited in [6; 7; 8] to simple rings (§§ 2 and 3). More precisely; if a
simple ring … fact for division rings, for the sake of self-containedness, we shall sketch it here. …

… While we have attempted to make this monograph as self-contained as possible, it has been
difficult in view of the limitations on the size of this book. To keep the book to a reasonable …

… When referring to a local ring we will often specify the maximal ideal, for example "Let 9, m
… with regular local rings we will use the following terminology: If R is a regular local ring and P …

… , if R\J is a simple ring, we may assume R is a local ring. … Let R be a right artinίan and local
ring. Then every projectίve … Let R be a right artinίan and local ring. We assume that every …

… If R is Arf, then J is stable and S is Arf since any local ring infinitely near S is also infinitely
near R. Assume (2), then we just need to show that any local ring B = RP with P a maximal …