New elements in Hilbert algebras
محورهای موضوعی : Transactions on Fuzzy Sets and Systems
Ardavan Najafi
1
(Department of Mathematics, Behbahan Branch, Islamic Azad University, Behbahan, Iran.)
کلید واژه: Hilbert algebras, commutator, Engel (involution) elements, left (right) $k$-Engel element.,
چکیده مقاله :
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.
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.
[1] Busneag D. A note on deductive systems of a Hilbert algebra. Kobe journal of mathematics. 1985; 2: 20-35.
[2] Chajda I, Hala R. Semilattice Structures. Heldermann Verlag: Research and Exposition in Mathematics; 2001.
[3] Chajda I, Hala R. Congruences and ideals in Hilbert algebras. Kyungpook Mathematical Journal. 1999; 2: 429-432. DOI: https://doi.org/10.1515/dema-2000-0202
[4] Diego A. Sur algbres de Hilbert. Collect. Logique Math. Ser. A. 1967; 21: 177-198.
[5] Jun YB, Nam JW, Hong SM. A note on Hilbert algebra. East Asian mathematical journal. 1994; 10(2): 279-285. DOI: https://doi.org/10.1142/S1793557109000303
[6] Jun YB, Park CH. Applications of soft sets in Hilbert algebras. Iranian Journal of Fuzzy Systems. 2009; 6(2): 7586. DOI: http://doi.org/10.22111/ijfs.2009.212
[7] Najafi A, Borumand Saeid A. Engel BCI-algebras: An application of left and right commutators. Mathematica Bohemica. 2021; 146(2): 133-150. DOI: http://doi.org/10.21136/MB.2020.0160-18
[8] Sergio A. Notes on bounded Hilbert algebras with supremum. Acta Scientiarum Mathematicarum. 2014; 80(1): 3-19. DOI: https://doi.org/10.14232/actasm-012-267-9
