New elements in Hilbert algebras
Subject Areas : Transactions on Fuzzy Sets and Systems
Ardavan
Najafi
1
(Department of Mathematics, Behbahan Branch, Islamic Azad University, Behbahan, Iran.)
Keywords: Hilbert algebras, commutator, Engel (involution) elements, left (right) $k$-Engel element.,
Abstract :
In this paper, the notion of commutator of elements of a Hilbert algebra are introduced and some properties are given. The notions of involution element and Engel element in Hilbert algebras are introduced. Many different characterizations of them are given. Then, left (right) $k$-Engel elements as a natural generalization of commutators are introduced, and we discuss Engel elements, which is defined by left and right commutators. Finally, we will also study relationships between these elements.
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