On the Prime Radical of a Hypergroupoid

Gursel Yesilot
2005 Journal of Mathematics and Statistics  
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
more » ... (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).
doi:10.3844/jmssp.2005.234.238 fatcat:3gzo4cv3nvhjpdwmsnhnihvwgq