Journal of Mathematics and Statistics

On the Prime Radical of a Hypergroupoid

Gürsel Yeşilot

DOI : 10.3844/jmssp.2005.234.238

Journal of Mathematics and Statistics

Volume 1, Issue 3

Pages 234-238

Abstract

In this study, we give definitions of a prime ideal, a s-semiprime ideal and a w-semiprime ideal for a hypergroupoid K. For an ideal A of K we show that radical of A (R(A)) can be represented as the intersection of all prime ideals of K containing A and we define a strongly A-nilpotent element. For any ideal A of K, we prove that R(A)=∩(s-semiprime ideals of K containing A)= ∩(w-semiprime ideals of K containing A)={strongly A nilpotent elements}. For an ideal B of K put B(o)=B and B(n+1)=(B(n))2. If a hypergroupoid K satisfies the ascending chain condition for ideals then (R(A))(n)⊆A for some n. For an ideal A of K we give a definition of right radical of A (R+(A)). If K is associative then R(A)=R+(A)=R_(A).

Copyright

© 2005 Gürsel Yeşilot. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.