We consider a strongly regular graph, G, and associate a three dimensional Euclidean Jordan algebra, V, to the adjacency matrix A of G. Then, by considering convergent series of Hadamard powers of the idempotents of the unique complete system of orthogonal idempotents of V, we establish new feasibility conditions for the existence of strongly regular graphs.

We consider association schemes with d classes and the underlying BoseMesner algebra, A . Then, by taking into account the relationship between the Hadamard and the Kronecker products of matrices and making use of some matrix techniques over the idempotents of the unique basis of minimal orthogonal idempotents of A , we prove some results over the Krein parameters of an association scheme.

Members of idempotents in (βN,+), especially those in the smallest ideal, have strong combinatorial properties. And the closure Γ of the set of idempotents has a simple combinatorial description. We investigate here the relationships among several subsets of βN that have simple combinatorial descriptions, as well as the semigroups they generate and their closures.

Let p be a prime number. This paper describes the primitive idempotents and prime spectrum of the crossed Burnside algebra of a finite group over a p-local ring. The main application is a formula for the block idempotents of the p-local Mackey algebra of the group, in terms of the corresponding blocks of the group algebra. Mathematics Subject Classification (2000): 19A22 20C20

In this paper we explore the topological properties of self-replicating, 3-dimensional manifolds, which are modeled by idempotents in (2+1)-cobordism category. We give a classification theorem for all such idempotents. Additionally, characterize biologically interesting ways self-replicating 3-manifolds can embed R3.

We give a criterion for when idempotents of a ring R which commute modulo the Jacobson radical J(R) can be lifted to commuting idempotents of R. If such lifting is possible, we give extra information about the lifts. A “half-commuting” analogue is also proven, and this is used to give sufficient conditions for a ring to have the internal exchange property. In particular, we show that if R/J(R) ...