  Constraints are given on the depth of diagonal subalgebras in generalized
triangular matrix algebras. The depth of the top subalgebra B = A /rad A in a
finite, connected, acyclic quiver algebra A over an algebraically closed field
K is then computed. Also the depth of the primary arrow subalgebra 1K + rad A =
B in A is obtained. The two types of subalgebras have depths 3 and 4
respectively, independent of the number of vertices. An upper bound on depth is
obtained for the quotient of a subalgebra pair.
