Vol. 32, No. 1, 1970

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On left QF 3 rings

Hiroyuki Tachikawa

Vol. 32 (1970), No. 1, 255–268

In this paper the following results are proved:

(i) Three classes of left QF-3 rings are closed under taking left quotient rings respectively.

(ii) A subcategory of left modules having dominant dimensions 2 over a right perfect left QF-3 ring R is equivalent to a category of all left fRf-modules, where f is a suitable idempotent of R.

(iii) In case a left QF-3 ring is obtained as the endomorphism ring of a generator, dominant dimensions (2) of modules are closely connected with the vanishing of Extfunctors.

(iv) Three classes of left and right QF-3 rings are identical in case of perfect rings.

Mathematical Subject Classification
Primary: 16.50
Received: 6 November 1968
Published: 1 January 1970
Hiroyuki Tachikawa