Geodesic
Prime Ideals in Regular Self-Injective Rings
Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 829-839

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Goodearl, K. R. Prime Ideals in Regular Self-Injective Rings. Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 829-839. doi: 10.4153/CJM-1973-085-3
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