Department of Mathematics Server University of Manitoba

Abstract: The fundamental Separativity Problem for von Neumann regular rings is shown to be equivalent to a linear algebra problem: for a field F, is there a "uniform formula" PAQ=D for diagonalising a 2x2 matrix A over the ring of nxn matrices over F independently of n? Here P and Q are required to be invertible matrices whose entries are fixed regular algebra expressions in the entries of A.