Simple axiomatization of reticulations on residuated lattices

We give a simple and independent axiomatization of reticulations on residuated latticesý, ýwhich were axiomatized by five conditions in [Cý. Mureşaný, ýThe reticulation of a residuated latticeý, ýBullý. ýMathý. ýSocý. ýSciý. ýMathý. ýRoumanieý ý51 (2008)ý, ýnoý. ý1ý, ý47--65]ý. ýMoreoverý, ýwe show that reticulations can be considered as lattice homomorphisms between residuated lattices and bounded distributive latticesý. ýConsequentlyý, ýthe result proved by Muresan in 2008ý, ýfor any two reticulattions (L1ý,ýλ1)ý,ý(L2ý,ýλ2) of a residuated lattice X there exists an isomorphism fý:ýL1→L2 such that f∘λ1=λ2ý, ýcan be considered as a homomorphism theoremý.