Continuous Rings and Rings of Quotients

Page, S. S.

Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 319-324

Résumé

Throughout R will denote an associative ring with identity. Let Zl(R) be the left singular ideal of R. It is well known that Zl(R) = 0 if and only if the left maximal ring of quotients of R, Q(R), is Von Neumann regular. When Zl(R) = 0, q(R) is also a left self injective ring and is, in fact, the injective hull of R. A natural generalization of the notion of injective is the concept of left continuous as studied by Utumi [4]. One of the major obstacles to studying the relationships between Q(R) and R is a description of J(Q(R)), the Jacobson radical of Q(R). When a ring is left continuous, then its left singular ideal is its Jacobson radical. This facilitates the study of the cases when either Q(R) is continuous or R is continuous.

Détail

DOI : 10.4153/CMB-1978-055-3