New Classes of Filters in Delta-Algebras

Azeez Lafta  Jaber; Shuker Mahmood  Khalil

doi:10.24996/ijs.2024.65.8.23

Authors

Azeez Lafta Jaber Department of Mathematics, College of Science University of Basrah, Basrah 61004, Iraq https://orcid.org/0000-0003-2569-7791
Shuker Mahmood Khalil Department of Mathematics, College of Science University of Basrah, Basrah 61004, Iraq https://orcid.org/0000-0002-7635-3553

DOI:

https://doi.org/10.24996/ijs.2024.65.8.23

Keywords:

δ-algebra, complete δ – filters, δ-ideals, regular δ-algebra, δ-subalgebra

Abstract

The main objective of this topic is to define new types of filters in algebra, such as filter and complete filter. Some theorems that establish the link between these filters were also presented and validated. Any filter in algebra is shown it is a complete filter. Furthermore, regular algebra is demonstrated as a new class of algebra. Additionally, this study introduces two new concepts such as complete ideal and normal. Also, any normal in regular algebra is demonstrated that it is a subalgebra. In addition, the connections between the complete ideal and the subalgebra is investigated. However, some instances are provided to clarify and bolster our results and findings.