  This article deals mostly with the following question: when is the classical
ring of quotients of a commutative ring a ring of stable range 1? We introduce
the concepts of a ring of (von Neumann) regular range 1, a ring of
semihereditary range 1, a ring of regular range 1, a semihereditary local ring,
a regular local ring. We find relationships between the introduced classes of
rings and known ones, in particular, it is established that a commutative
indecomposable almost clean ring is a regular local ring. A commutative any
ring of idempotent regular range 1 is an almost clean ring. It is shown that
any commutative indecomposable almost clean Bezout ring is an Hermite ring, any
commutative semihereditary ring is a ring of idempotent regular range 1. The
classical ring of quotients of a commutative Bezout ring is a (von Neumann)
regular local ring if and only if R is a commutative semihereditary local ring.
