  In this paper we prove relationships between two generalizations of
commutative valuation theory for noncommutative central simple algebras: (1)
Dubrovin valuation rings; and (2) the value functions called gauges introduced
by Tignol and Wadsworth in [TW1] and [TW2]. We show that if v is a valuation on
a field F with associated valuation ring V and v is defectless in a central
simple F-algebra A, and C is a subring of A, then the following are equivalent:
(a) C is the gauge ring of some minimal v-gauge on A, i.e., a gauge with the
minimal number of simple components of C/J(C); (b) C is integral over V with C
= B_1 \cap ... \cap B_xi$ where each B_i is a Dubrovin valuation ring of A with
center V, and the B_i satisfy Graeter's Intersection Property. Along the way we
prove the existence of minimal gauges whenever possible and we show how gauges
on simple algebras are built from gauges on central simple algebras.
