TY  - JOUR
AU  - Yeşilot, Gürsel 
PY  - 2005
TI  - On the Prime Radical of a Hypergroupoid
JF  - Journal of Mathematics and Statistics
VL  - 1
IS  - 3
DO  - 10.3844/jmssp.2005.234.238
UR  - https://thescipub.com/abstract/jmssp.2005.234.238
AB  - 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).