Zero-Dimensional Subrings of Commutative Rings

Robert Gilmer

We consider various conditions of the sets of zero-dimensional, Artinian, and von Neumann regular subrings of a commutative ring. Section 1 treats questions of existence of such rings, Section 2 deals with the situation in which all subrings belong to one of the three classes, and Section 3 is concerned with the behavior of the sets under intersection. In Section 4 we give a brief survey of some generalizations and extensions of results of Sections 1--3, as well as some related results.