Pure filters and topological spaces on triangle algebras

Articles in Press

Document Type : Research Paper

Authors

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.

10.48308/cgasa.2024.235170.1477

Abstract

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.

Keywords

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References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 10 January 2025

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