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

<p>In this article, we study relationships between closure operators and hoops. We investigate the properties of closure operators and hoop-homomorphism on hoops. We show that the image of a closure operator on a hoop is isomorphic to a quotient hoop. In addition, we define the notion of closure operator on ideals of hoop and investigate some properties of it and some related results are proved. We define proper closer operators on ideals of hoop and we show that the set of all proper closure operators on hoops makes a bounded lattice by some operations.</p>
</abstract>

In this article, we study relationships between closure operators and hoops. We investigate the properties of closure operators and hoop-homomorphism on hoops. We show that the image of a closure operator on a hoop is isomorphic to a quotient hoop. In addition, we define the notion of closure operator on ideals of hoop and investigate some properties of it and some related results are proved. We define proper closer operators on ideals of hoop and we show that the set of all proper closure operators on hoops makes a bounded lattice by some operations.

Closure operators on hoops

Department of Mathematics, Faculty of Mathematical Sciences

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

{"article-title":"Closure operators on hoops"}

In this article, we study relationships between closure operators and hoops. We investigate the properties of closure operators and hoop-homomorphism on hoops....

Closure operators on hoops

Published Online: May 27, 2024

Page range: 85 - 104

Received: Oct 28, 2022

Accepted: Mar 15, 2023

DOI: https://doi.org/10.2478/auom-2024-0005

Keywords
Hoop, ideal, maximal and prime ideals, closure operators

© 2024 R.A. Borzooei, published by Sciendo

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

Closure operators on hoops

Published Online: May 27, 2024

Page range: 85 - 104

Received: Oct 28, 2022

Accepted: Mar 15, 2023

DOI: https://doi.org/10.2478/auom-2024-0005

KeywordsHoop, ideal, maximal and prime ideals, closure operators

© 2024 R.A. Borzooei, published by Sciendo

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

Keywords
Hoop, ideal, maximal and prime ideals, closure operators