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**hamidr** Drexel how do I check that? how do I check if zero*any element is in zero ideal, then there is no other element that * any element is in zero ideal

the problem that I am facing in abstract algebra , is that everything is being said equivalence to each other, but then there is no method given to check any of those equivalent relations. it is true that if zero ideal is not prime, then we will have only zero as the element in the ideal therefore zero is the only zero in the ring. but how can you be sure there it is prime ideal?

and I am assuming the ring that have zero divisor are not domains, so that they are not integral domain nor a PID or UFD.