Vol. 48, No. 2, 1973

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Idealizers and nonsingular rings

Kenneth R. Goodearl

Vol. 48 (1973), No. 2, 395–402

This paper deals with the relationship between a ring T and the idealizer R of a right ideal M of T. [The ring R is the largest subring of T which contains M as a two-sided ideal.] Assuming M to be a finite intersection of maximal right ideals of T, the properties of T and R are shown to be very similar. The main theorem of the first section shows that under these hypotheses the right global dimensions of T and R almost always coincide. In the second section, where T is assumed to be a nonsingular ring, the maior theorem asserts that the singular submodule of every R-module is a direct summand if and only if the corresponding property holds for T-modules.

Mathematical Subject Classification
Primary: 16A60
Received: 11 February 1972
Revised: 23 March 1973
Published: 1 October 1973
Kenneth R. Goodearl
University of California, Santa Barbara
Santa Barbara CA
United States