  We investigate criteria for von-Neumann finiteness and reversibility in some
classes of non-associative algebras. We show that all finite-dimensional
alternative algebras, as well as all algebras obtained from the real numbers
via the standard Cayley-Dickson doubling process, are von-Neumann finite.
Precise criteria for von-Neumann finiteness and reversibility of involutive
algebras are given, in terms of isomorphism types of their 3-dimensional
subalgebras.
