Results in L-algebras

We study some classes of L-algebras and we give characterizations of commutative KL-algebras and CL-algebras. It is proved that any commutative KL-algebra is a BCK-algebra and any self-similar CL-algebra is commutative. The commutative ideals are defined and studied, and it is proved that a CL-algebra is commutative if and only if all its ideals are commutative. We also present the L-algebras arising from other structures, such as BCK-algebras, pseudo MV-algebras, pseudo BL-algebras, pseudo-hoops, bounded Rl-monoids, BE-algebras, Hilbert algebras.