TY - JOUR
ID - 985
TI - Simple axiomatization of reticulations on residuated lattices
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Kondo, M.
AD - Department of mathematics, School of System Design and Technolodgy, Tokyo Denki University, Japan.
Y1 - 2017
PY - 2017
VL - 43
IS - 3
SP - 943
EP - 949
KW - Reticulation
KW - residuated lattice
KW - principal filter
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_985.html
L1 - http://bims.iranjournals.ir/article_985_6b7c6fb69b7eff043f603bf53907c367.pdf
ER -