IDEALS OF RESIDUATED LATTICES

In this article, we study ideals in residuated lattice and present a characterization theorem for them. We investigate some related results between the obstinate ideals and other types of ideals of a residuated lattice, likeness Boolean, primary, prime, implicative, maximal and circle dot-prime ideals. Characterization theorems and extension property for obstinate ideal are stated and proved. For the class of circle dot-residuated lattices, by using the circle dot-prime ideals we propose a characterization, and prove that an ideal is an circle dot-prime ideal iff its quotient algebra is an circle dot-residuated lattice. Finally, by using ideals, the class of Noetherian (Artinian) residuated lattices is introduced and Cohen's theorem is proved.