Engel BCI-algebras: an application of left and right commutators
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2021-07-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/146/2/mb146_2_3.pdf |
| Summary: | 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. |
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| ISSN: | 0862-7959 2464-7136 |