Abstract :
We give a simple and independent axiomatization of reticulations on residuated lattices, which were axiomatized by five conditions in [C. Mureşan, The reticulation of a residuated lattice, Bull. Math. Soc. Sci. Math. Roumanie 51 (2008), no. 1, 4765]. Moreover, we show that reticulations can be considered as lattice homomorphisms between residuated lattices and bounded distributive lattices. Consequently, the result proved by Muresan in 2008, for any two reticulattions (L_1, lambda_1), (L_2, lambda_2) of a residuated lattice X there exists an isomorphism f: L_1 to L_2 such that fcirc lambda_1 = lambda_2, can be considered as a homomorphism theorem.
