In this paper we consider the problem of routing messages in a network of processors conngured as a chordal ring. In particular we refer to the Boolean Routing model, and we introduce a new routing function for unidirectional and bidirectional chordal rings with degree four. This function requires O(n log n) bits of storage and O(n) time to compute, in the worst case. We also study some relatio...

A Boolean ring satisfies the identity x2 = x which, of course, implies the identity x2y − xy2 = 0. With this as motivation, we define a subBoolean ring to be a ring R which satisfies the condition that x2y−xy2 is nilpotent for certain elements x, y of R. We consider some conditions which imply that the subBoolean ring R is commutative or has a nil commutator ideal. Mathematics Subject Classific...

1. Introduction. Boolean rings (or generalized Boolean algebras), defined by Stone, are rings in which every element is idempotent. Sets of postulates for these rings have been given by Stone(2) and by Stabler(8). I give in this paper a number of additional postulate-sets for such rings. The sets are all expressed in terms of ring addition and multiplication. Stone's postulates for Boolean ring...