The use of balanced modules in representation theory

The minimal faithful module for an algebra A with dominant dimension at least 2.
Morita equivalence,
Tilting theory,
Schur-Weyl duality, Morita duality, Howe duality, ...

To say that an A-module M is balanced asserts that knowing M one can recover the ring A/Ann(M) over which M is defined
(here Ann(M) is the annihilator of M).

Concerning balanced modules, an unpublished manuscript has to be mentioned:
Tachikawa: QF-1 algebras with radicals of square zero.
There are two main results:

For k algebraically closed, Tachikawa provides a characterization of the QF-1 k-algebras A with (rad A)² = 0.
In particular it is shown: These algebras are of local-colocal representation type.
The construction of a local artinian ring which is balanced, but not uniserial
(thus this is a counter example to a conjecture by Jans).
The constructed algebra is of local-colocal representation type.
and it is stably equivalent to a hereditary algebra of type B₂.