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.
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