Abstract
In this paper, we first introduce the notion of Stonean implicative filter in Hilbert algebra and study it in detail. Finally, we introduce a Stonean Hilbert algebra and investigate its properties, we prove that, H is a Stonean Hilbert algebra if and only if the set of all regular elements of H is a Stonean Hilbert algebra. By the diagrams, we summarize the results of this paper and give the relationships between all types of filters in a Hilbert algebra. Also, we give the relationships between Hilbert algebra and some of algebraic structures.
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