<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we define the concepts of Engel, nilpotent and solvable <italic>BCI</italic>-algebras and investigate some of their properties. Specially, we prove that any <italic>BCK</italic>-algebra is a 2-Engel. Then we define the center of a <italic>BCI</italic>-algebra and prove that in a nilpotent <italic>BCI</italic>-algebra <italic>X</italic>, each minimal closed ideal of <italic>X</italic> is contained in the center of <italic>X</italic>. In addition, with some conditions, we show that every finite <italic>BCI</italic>-algebra is solvable. Finally, we investigate the relations among Engel, nilpotent and solvable <italic>BCI</italic>(<italic>BCK</italic>)-algebras.</p></abstract>

In this paper, we define the concepts of Engel, nilpotent and solvable BCI-algebras and investigate some of their properties. Specially, we prove that any BCK-algebra is a 2-Engel. Then we define the center of a BCI-algebra and prove that in a nilpotent BCI-algebra X, each minimal closed ideal of X is contained in the center of X. In addition, with some conditions, we show that every finite BCI-algebra is solvable. Finally, we investigate the relations among Engel, nilpotent and solvable BCI(BCK)-algebras.

Engel, Nilpotent and Solvable BCI-algebras

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Engel, Nilpotent and Solvable BCI-algebras"}

In this paper, we define the concepts of Engel, nilpotent and solvable BCI-algebras and investigate some of their properties. Specially, we prove that any...

Engel, Nilpotent and Solvable BCI-algebras

Published Online: Mar 02, 2019

Page range: 169 - 192

Received: Jan 30, 2018

Accepted: May 08, 2018

DOI: https://doi.org/10.2478/auom-2019-0009

Keywords
BCI-algebra, Engel BCI-algebra, nilpotent BCI-algebra, solvable BCI-algebra

© 2019 Elahe Mohammadzadeh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Engel, Nilpotent and Solvable BCI-algebras

Published Online: Mar 02, 2019

Page range: 169 - 192

Received: Jan 30, 2018

Accepted: May 08, 2018

DOI: https://doi.org/10.2478/auom-2019-0009

KeywordsBCI-algebra, Engel BCI-algebra, nilpotent BCI-algebra, solvable BCI-algebra

© 2019 Elahe Mohammadzadeh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
BCI-algebra, Engel BCI-algebra, nilpotent BCI-algebra, solvable BCI-algebra