Algebraic structure of association schemes of prime order

Algebraic structure of association schemes of prime order

Finite groups of prime order must be cyclic. It is natural to ask what about association schemes of prime order. In this paper, we will give an answer to this question. An association scheme of prime order is commutative, and its valencies of nontrivial relations and multiplicities of nontrivial irreducible characters are constant. Moreover, if we suppose that the minimal splitting field is an ...

Association schemes of prime order and their splitting fields

Algebraic and topological aspects of quasi-prime ideals

In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is pro...

Commutativity of association schemes of prime square order having non-trivial thin closed subsets

Through a study of the structure of the modular adjacency algebra over a field of positive characteristic p for a scheme of prime order p and utilizing the fact that every scheme of prime order is commutative, we show that every association scheme of prime square order having a non-trivial thin closed subset is commutative.

Classification of Association Schemes of Small Order

This paper enumerates the isomorphism classes of association schemes of order 20–28 by using the computer. It also classi es all the association schemes of order 24–28 whether their automorphism groups are transitive or not, and whether they are group case or not. Some more properties of the obtained association schemes are computed. c © 2002 Elsevier Science B.V. All rights reserved.