Prime and primary ideals on L-algebras

In this paper, we review L-algebras and CL-algebras, focusing in particular on the notion of a prime ideal. We establish criteria for a prime ideal and analyze the relationship between maximal and prime ideals. In addition, we define prime ideals in CL-bounded algebras, and state conditions for an ideal to be prime in a self-distributing bounded L-algebra. We introduce the radical of an ideal and show that if its radical is maximal, then it is a prime ideal. Finally, we establish conditions under which every prime ideal in an L-algebra is primary.

کلیدواژه ها:

L-algebra ، Local ، Primary ideal ، Prime ideal ، Radical of an ideal ، Self-distributive L-algebra