New prime filter types in BL-algebras

Key Points

• The aim is to introduce and explore new types of filters in BL-algebras, particularly α-prime and S-prime filters.
• Defined α-prime and S-prime filters in the context of BL-algebras based on an endomorphism and a closed subset.
• Examined examples to illustrate the new concepts and their fundamental properties.
• Studied the relationships between α-prime filters, S-prime filters, maximal filters, and traditional prime filters.
• Introduced two new classes of filters, α-prime and S-prime, that generalize earlier concepts in BL-algebras.
• Provided initial characterizations and properties of these filters, showing distinct behaviors compared to traditional prime filters.
• Established connections among all introduced filters, enhancing the understanding of their structural properties in BL-algebras.