| Title:
|
Engel BCI-algebras: an application of left and right commutators (English) |
| Author:
|
Najafi, Ardavan |
| Author:
|
Borumand Saeid, Arsham |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
146 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
133-150 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
(left and right) Engel element |
| Keyword:
|
commutator |
| Keyword:
|
Engel BCI-algebra |
| MSC:
|
03G25 |
| MSC:
|
06F35 |
| DOI:
|
10.21136/MB.2020.0160-18 |
| . |
| Date available:
|
2021-05-20T13:52:37Z |
| Last updated:
|
2021-06-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148928 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
[10] Najafi, A., Saeid, A. Borumand: Solvable BCK-algebras.Çankaya Univ. J. Sci. Eng. 11 (2014), 19-28. |
| Reference:
|
[11] Najafi, A., Saeid, A. Borumand, Eslami, E.: Commutators in BCI-algebras.J. Intell. Fuzzy Syst. 31 (2016), 357-366. Zbl 1367.06009, 10.3233/IFS-162148 |
| Reference:
|
[12] Najafi, A., Saeid, A. Borumand, Eslami, E.: Centralizers of BCI-algebras.(to appear) in Miskolc Math. Notes. |
| Reference:
|
[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. Zbl 0708.9742, MR 3896549 |
| . |
