Radical of filters on hoops
نویسندگان
1 Hatef Higher Education Institute, Zahedan, Iran
2 Shahid Beheshti University
3 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
doi
10.22111/ijfs.2023.7661چکیده
In this paper, by using the notion of prime filter, we show representation theorem of hoops and we prove that every nontrivial ∨-hoop is a subdirect product of hoop-chains. In the following, by using the concept of maximal filter of hoops, we introduce radical of hoops. Then some equivalence definitions of it and some related properties are investigated. Then by using this notion, we introduce the concepts of r-filters and p-filters on hoops and the relation between them and other filters of hoops are investigated. Finally, by using p-filters on hoops, we define new open sets on hoop that could be used to construct a Zarisky topology.
