Von-Neumann finiteness and reversibility in some classes of   non-associative algebras
  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. 
Erik Darp\"o and Patrik Nystedt
math.RA