%0 Journal Article %T Simple axiomatization of reticulations on residuated lattices %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Kondo, M. %D 2017 %\ 06/01/2017 %V 43 %N 3 %P 943-949 %! Simple axiomatization of reticulations on residuated lattices %K Reticulation‎ %K ‎residuated lattice‎ %K ‎principal filter‎ %R %X ‎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, ‎47--65]‎. ‎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 $f\circ \lambda_1 = \lambda_2$‎, ‎can be considered as a homomorphism theorem‎. %U http://bims.iranjournals.ir/article_985_6b7c6fb69b7eff043f603bf53907c367.pdf