Filters in Residuated Algebras
نویسندگان
چکیده
In this paper we study the filters in residuated algebras. We investigate the properties of the filters. We also define a congruence relation on the residuated algebras corresponding to a given filter and study its properties. We define the quotient algebra induced by this relation. We prove that this is also a residuated algebra with special properties.
منابع مشابه
Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices
At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...
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