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Closure operators on hoops Cover

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.

DOI: https://doi.org/10.2478/auom-2024-0005 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 85 - 104
Submitted on: Oct 28, 2022
Accepted on: Mar 15, 2023
Published on: May 27, 2024
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2024 R.A. Borzooei, M. Aaly Kologani, G.R. Rezaei, M. Mohseni Takallo, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.