It has been known for some years that entanglement entropy obtained from partial trace does not provide the correct entanglement measure when applied to systems of identical particles. Several criteria have been proposed that have the drawback of being different according to whether one is dealing with fermions, bosons or distinguishable particles. In this Letter, we give a precise and mathematically natural answer to this problem. Our approach is based on the use of the more general idea of restriction of states to subalgebras. It leads to a novel approach to entanglement, suitable to be used in general quantum systems and specially in systems of identical particles. This settles some recent controversy regarding entanglement for identical particles. The prospects for applications of our criteria are wide-ranging, from spin chains in condensed matter to entropy of black holes.