Associated Prime Ideal and Minimal Prime Ideal of an Ideal of an L-Subring

In this paper, a systematic theory for the ideals of an L-ring $L(\mu ,R)$ has been developed. Earlier the authors have introduced the concepts of prime ideals, semiprime ideals, primary ideals, and radical of an ideal in an L-ring. They have also introduced and discussed the notion of a maximal ideal in different papers wherein several results pertaining to these notions have been proved. In this paper, the concepts of associated prime ideal, minimal prime ideal, and that of irreducibility of an ideal in an L-ring have been introduced, which in fact, are the continuation of authors’ previous works in the theory of ideals in L-rings.