Vol. 39, No. 1, 1971

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Rings of quotients and π-regularity

Robert Raphael

Vol. 39 (1971), No. 1, 229–233

Throughout this paper rings are understood to be commutative with 1, and subrings are understood to have the same identity as their over-rings. Familiarity with the Utumi-Lambek concept of complete ring of quotients Q(R), of a commutative ring R, is assumed. Q(R) is commutative and it contains a copy of the classical ring of quotients of R (denoted QC1(R)), obtained by localizing R at its set of nonzero-divisors. Any ring lying between R and Q(R) is called a ring of quotients of R. R is π-regular if for r R there exists !r′∈ R and a positive integer n such that rn = (rn)2r. This paper investigates the question: if Q(R) is πregular, under what conditions are all rings of quotients of -regular?

Mathematical Subject Classification 2000
Primary: 13B99
Received: 12 May 1970
Published: 1 October 1971
Robert Raphael