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 π− regular, under what conditions are all rings
of quotients of Rπ-regular?
