%0 Journal Article
%T Simple axiomatization of reticulations on residuated lattices
%J Bulletin of the Iranian Mathematical Society
%I Springer and the 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 $fcirc lambda_1 = lambda_2$, can be considered as a homomorphism theorem.
%U http://bims.iranjournals.ir/article_985_6b7c6fb69b7eff043f603bf53907c367.pdf