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.
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

[1] Abdollahi, A.: Engel graph associated with a group. J. Algebra 318 (2007), 680-691. | DOI | MR | JFM

[2] Abdollahi, A.: Engel elements in groups. Groups St. Andrews 2009 in Bath. Vol. I. London Mathematical Society Lecture Note Series 387. Cambridge University Press, Cambridge (2011), 94-117 C. M. Campbell, et al. | DOI | MR | JFM

[3] Dudek, W. A.: On group-like BCI-algebras. Demonstr. Math. 21 (1988), 369-376. | DOI | MR | JFM

[4] Dudek, W. A.: Finite BCK-algebras are solvable. Commun. Korean Math. Soc. 31 (2016), 261-262. | DOI | MR | JFM

[5] Huang, Y.: BCI-Algebras. Science Press, Beijing (2006).

[6] Iséki, K.: An algebra related with a propositional calculus. Proc. Japan Acad. 42 (1966), 26-29. | DOI | MR | JFM

[7] Iséki, K.: On BCI-algebras. Math. Semin. Notes, Kobe Univ. 8 (1980), 125-130. | MR | JFM

[8] Lei, T., Xi, C.: $p$-radical in BCI-algebras. Math. Jap. 30 (1985), 511-517. | MR | JFM

[9] Najafi, A.: Pseudo-commutators in BCK-algebras. Pure Math. Sci. 2 (2013), 29-32. | DOI | JFM

[10] Najafi, A., Saeid, A. Borumand: Solvable BCK-algebras. Çankaya Univ. J. Sci. Eng. 11 (2014), 19-28.

[11] Najafi, A., Saeid, A. Borumand, Eslami, E.: Commutators in BCI-algebras. J. Intell. Fuzzy Syst. 31 (2016), 357-366. | DOI | JFM

[12] Najafi, A., Saeid, A. Borumand, Eslami, E.: Centralizers of BCI-algebras. (to appear) in Miskolc Math. Notes.

[13] Najafi, A., Eslami, E., Saeid, A. Borumand: A new type of nilpotent BCI-algebras. An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 64 (2018), 309-326 \99999MR99999 3896549 \filbreak. | MR | JFM

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