Commutative, Engel and Solvable EQ-Algebras

Akbar Paad ()
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Akbar Paad: Department of Mathematics, University of Bojnord, Bojnord, Iran

New Mathematics and Natural Computation (NMNC), 2022, vol. 18, issue 01, 43-60

Abstract: The main goal of this paper is to introduce commutative, Engel and solvable EQ-algebras. To begin with, the notion of commutators of two elements in EQ-algebras is introduced and several properties of them are obtained. In this paper, the notions of commutative, Engel and solvable EQ-algebras are introduced and some of their properties are investigated. Specially, it is proved that any good EQ-algebra is a 2-Engel EQ-algebra. In addition, the relation between fantastic filters and good commutative EQ-algebras is investigated and it is proved that a filter F of good EQ-algebra L is fantastic if and only if the quotient EQ-algebra L F is commutative. Finally, it is proved that if an EQ-algebra separated, then it is a commutative EQ-algebra if and only if it is solvable if and only if it is a 1-Engel EQ-algebra.

Keywords: EQ-algebra; commutative (n-Engel; solvable) EQ-algebra; commutator of two elements (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S1793005722500041

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