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Study of Hilbert algebras in point of filters. (English) Zbl 1389.03031

Summary: The aim of this work is to introduce some types of filters in Hilbert algebras. Some theorems are stated and proved which determine the relationship between these notions and other filters of Hilbert algebra and by some examples we show that these concepts are different. The relationships between these filters and quotient algebras that are constructed via these filters are described.

MSC:

03G25 Other algebras related to logic
06F35 BCK-algebras, BCI-algebras
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