Pure filters and topological spaces on triangle algebras

نویسندگان
Koguep Njionou, Blaise Bleriot ID 1
Demlabi Pamba Anani, Franclin ID 2
Tallee Kakeu, Ariane Gabriel ID 3
Lele, Celestin ID 4

1 Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, Cameroon

2 Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, Cameroon

3 Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, Cameroon.

4 Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, Cameroon

doi
10.48308/cgasa.2024.235170.1477
چکیده

In this paper, we delve into the lattice of filters of a triangle algebra. Moreover, we establish the prime filter theorem, and investigate the algebraic structure of the set of co-annihilators of a triangle algebra. In addition, we explore the concept of  pure filter within the framework of  triangle algebras. Furthermore, we describe the topological properties of the prime filter space of a triangle algebra by equipping the lattice of prime filters with the Zariski topology. Thanks to the notion of pure filters in triangle algebras, we also provide a characterization of the open stable sets with respect to the stable topology, a topology that is coarser than the Zariski topology.

کلیدواژه‌ها
Triangle algebra, filter, pure filter, Zariski topology, stable topology