Geodesic
Engel BCI-algebras: an application of left and right commutators
Mathematica Bohemica, Tome 146 (2021) no. 2, pp. 133-150

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We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of $n$-Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is defined by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type $2$ is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is proved that $1$-Engel BCI-algebras are exactly the commutative BCI-algebras.
DOI : 10.21136/MB.2020.0160-18
Classification : 03G25, 06F35
Keywords: (left and right) Engel element; commutator; Engel BCI-algebra 
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Najafi, Ardavan; Borumand Saeid, Arsham. Engel BCI-algebras: an application of left and right commutators. Mathematica Bohemica, Tome 146 (2021) no. 2, pp. 133-150. doi: 10.21136/MB.2020.0160-18

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