Engel BCI-algebras: an application of left and right commutators

Ardavan Najafi; Arsham Borumand Saeid

Mathematica Bohemica (2021)

  • Volume: 146, Issue: 2, page 133-150
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Najafi, Ardavan, and Borumand Saeid, Arsham. "Engel BCI-algebras: an application of left and right commutators." Mathematica Bohemica 146.2 (2021): 133-150. <http://eudml.org/doc/298255>.

@article{Najafi2021,
abstract = {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.},
author = {Najafi, Ardavan, Borumand Saeid, Arsham},
journal = {Mathematica Bohemica},
keywords = {(left and right) Engel element; commutator; Engel BCI-algebra},
language = {eng},
number = {2},
pages = {133-150},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Engel BCI-algebras: an application of left and right commutators},
url = {http://eudml.org/doc/298255},
volume = {146},
year = {2021},
}

TY - JOUR
AU - Najafi, Ardavan
AU - Borumand Saeid, Arsham
TI - Engel BCI-algebras: an application of left and right commutators
JO - Mathematica Bohemica
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 146
IS - 2
SP - 133
EP - 150
AB - 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.
LA - eng
KW - (left and right) Engel element; commutator; Engel BCI-algebra
UR - http://eudml.org/doc/298255
ER -

References

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  10. Najafi, A., Saeid, A. Borumand, Solvable BCK-algebras, Çankaya Univ. J. Sci. Eng. 11 (2014), 19-28. (2014) 
  11. Najafi, A., Saeid, A. Borumand, Eslami, E., 10.3233/IFS-162148, J. Intell. Fuzzy Syst. 31 (2016), 357-366. (2016) Zbl1367.06009DOI10.3233/IFS-162148
  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 9999MR99999 3896549 . (2018) MR3896549

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