Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices

Authors

1 Department of Mathematics, Faculty of Mathematics and Natural Sci- ences, University of Craiova, Craiova, Romania

2 Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Craiova, Craiova, Romania

Abstract

At present, the filter theory of $BL$textit{-}algebras has been widely
studied, and some important results have been published (see for example
cite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such as
cite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory in
the more general setting of residuated lattices is done, generalizing that
for $BL$textit{-}algebras. Note that filters are also characterized by
various types of fuzzy sets. Most of such characterizations is trivial but
some are nontrivial, for example characterizations obtained in cite{xm}.
Both situation have revealed a rich range of classes of filters: Boolean,
implicative, Heyting, positive implicative, fantastic (or MV-filter), etc.
In this paper we work in the general cases of residuated lattices and put in
evidence new types of filters in a residuated lattice (in the spirit of cite
{mvl}): semi-G-filterstextit{, }Stonean filters, divisible filters,
BL-filters and regular filters.

Keywords


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