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Prime Ideals in Regular Self-Injective Rings

Published online by Cambridge University Press:  20 November 2018

K. R. Goodearl
K. R. Goodearl*
Affiliation:
University of Chicago, Chicago, Illinois; University of Utah, Salt Lake City, Utah
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Although the notion of the maximal quotient ring of a nonsingular ring has been around for some time, not much is known about its structure in general beyond the important theorems of Johnson and Utumi [4; 11] that it is von Neumann regular and self-injective. The purpose of this paper is to study the structure of such a regular, self-injective ring R by looking at its prime ideals. Initially, we show that the primes of R separate into two types, called ‘'essential” and ‘“closed”, and that for any prime P, the two-sided ideals in the ring R/P are linearly ordered.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 829 - 839
Copyright
Copyright © Canadian Mathematical Society 1973

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