@article { author = {Kondo, M.}, title = {On residuated lattices with universal quantifiers}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {41}, number = {4}, pages = {923-929}, year = {2015}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {We consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $X$, $(X, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $X$. We also show that, for a strong residuated lattice $X$, $bigcap {P_{lambda} ,|,P_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong residuated lattice is a subdirect product of a strong residuated lattice with a universal quantifier ${ X/P_{lambda} }$, where $P_{lambda}$ is a prime $m$-filter. As a corollary of this result, we prove that every strong monadic MTL-algebra (BL- and MV-algebra) is a subdirect product of linearly ordered strong monadic MTL-algebras (BL- and MV-algebras, respectively).}, keywords = {Residuated lattice‎,‎universal quantifier‎,‎{\it m}-filter‎}, url = {http://bims.iranjournals.ir/article_662.html}, eprint = {http://bims.iranjournals.ir/article_662_1669854ce28fe0f5c70995f42d449e5f.pdf} }