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On the Prime Radical of a Hypergroupoid

2005
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Journal of Mathematics and Statistics
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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

doi:10.3844/jmssp.2005.234.238
fatcat:3gzo4cv3nvhjpdwmsnhnihvwgq