<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset.</p>
<p>Moreover, the notion of strongly right (left) independent subset is considered. It is proved that there exists a groupoid having a strongly right independent 2-set. Finally, we discuss the notion of dynamic elements with independence.</p>
</abstract>

In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset.
Moreover, the notion of strongly right (left) independent subset is considered. It is proved that there exists a groupoid having a strongly right independent 2-set. Finally, we discuss the notion of dynamic elements with independence.

Independence concepts for groupoids

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"Independence concepts for groupoids"}

In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is...

Independence concepts for groupoids

Published Online: Jul 25, 2023

Page range: 87 - 98

Received: Nov 16, 2022

Accepted: May 31, 2023

DOI: https://doi.org/10.2478/aupcsm-2023-0007

© 2023 Akbar Rezaei et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.