@article {
author = {Kondo, M.},
title = {Simple axiomatization of reticulations on residuated lattices},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {43},
number = {3},
pages = {943-949},
year = {2017},
publisher = {Springer and the Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
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, 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.},
keywords = {Reticulation,residuated lattice,principal filter},
url = {http://bims.iranjournals.ir/article_985.html},
eprint = {http://bims.iranjournals.ir/article_985_6b7c6fb69b7eff043f603bf53907c367.pdf}
}