Springer and the Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43320170601Simple axiomatization of reticulations on residuated lattices943949985ENM.KondoDepartment of mathematics, School of System Design and Technolodgy, Tokyo Denki University, Japan.Journal Article20151014We 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 $fcirc lambda_1 = lambda_2$, can be considered as a homomorphism theorem.http://bims.iranjournals.ir/article_985_6b7c6fb69b7eff043f603bf53907c367.pdf