A lattice-theoretical approach to extensions of filters in algebras of substructural logic

Document Type : Original Article


1 Department of Mathematical Methods in economy, Faculty of Economics, VSB-Technical University Ostrava, Sokolska 33, 701 21 Ostrava, Czech Republic

2 Department of Algebra and Geometry, Faculty of Sciences, Palacky University, 17. listopadu 12, 771 46 Olomouc, Czech Republic


Commutative bounded integral residuated lattices (residutaed lattices, in short) form a large class of algebras containing algebras which are algebraic counterparts of certain propositional fuzzy logics. The paper deals with the so-called extended filters of filters of residuated lattices. It is used the fact that the extended filters of filters associated with subsets coincide with those associated ones with corresponding filters. This makes it possible to investigate the set of all extended filters of residuated lattices within the Heyting algebras of their filters by means of the structural methods of the theory of such algebras.