  Let R be a commutative ring. A not necessarily commutative R-algebra A is
called futile if it has only finitely many R-subalgebras. In this article we
relate the notion of futility to familiar properties of rings and modules. We
do this by first reducing to the case where A is commutative. Then we refine
the description of commutative futile algebras from Dobbs, Picavet and
Picavet-L'hermite.
