Mary Wright

Krull dimension in serial rings

Abstract The main result of this paper is that if a serial ring R has right Krull dimension α, then it also has left Krull dimension α.

Decompositions of D1 Modules

Continuity and quasicontinuity for modules may be viewed as generalizations of quasi-injectivity. A key property of quasi-continuous modules is that complements are summands. Modules with this special property are called extending modules or C1 modules. We investigate decomposition properties of dual-extending (D1) modules, those modules which are supplemented and for which each supplement is a summand. The notions of hollowness and dual Goldie dimension play a prominent role. Our results are analogous to results for extending modules developed by Camillo and Yousif.