  The dominant dimension of algebras in the class A of 1-quasi-hereditary
algebras is at least two. By the Morita-Tachikawa Theorem this implies that A
is related to a certain class B of algebras via bimodules satisfying the double
centralizer condition. In this paper we specify the class B and the modules
over algebras in B connected with A.
  The class A is not closed under taking the Ringel-dual. However the dominant
dimension of the Ringel-dual R(q) of a 1-quasi-hereditary algebra q is at least
two. This fact induces a corresponding concept of modules over algebras in B
which yield the algebras q and R(q) for q in A.
