Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 546
The S-flat topology
Mohamed Aqalmoun
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
February 28, 2022
March 03, 2443
April 15, 2443

Abstract: For a commutative ring R with non-zero unit and a multiplicatively closed subset S of R, we introduce a new topology on the S-prime spectrum Spec_S R of R called the S-flat topology which is a generalization of the flat topology. If we take S a subset of the set of units in R, then the two topologies are equal. The algebraic descriptions of the topological properties like compactness irreducibility and Noetherianess are investigated. For instance, it is shown that every closed S-Zarisky is quasi-compact with respect to the S-flat topology and every S-flat irreducible closed subset has a ...