Abstract
In hemiring, out of six prime ideals [PI(S)], it is established that it reduces in to four prime ideals [PI(S)] when the ideal is k - prime ideal [KPI(S)]. It is proved that the prime k – ideals [PKI(S)] coincide with 1 - prime ideal [IPI(S)], 2 - prime ideal [2PI(S)] when the ideal [I(S)] is k – ideal [KI(S)]. It is established that thirteen necessary and sufficient conditions for a k – ideal [KI(S)] to be prime k – ideal [PKI(S)] (1 – prime ideal [1PI(S)], 2 - prime ideal [2PI(S)]). Examples are given to validate our results.
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