Abstract
In this paper, we introduced a new type of algebra, namely a ƁD-algebra. and some of them its properties are discussed in this type. Also, we introduced some theorems and examples of ƁD-algebra. Its properties differ from the rest of the other types of algebras. We tried to connect it with other types of algebras. We have also introduced a new type of ideals this type of algebra. and have tried to relate it to other ideals through the properties and theorems. Also, we have define a new type of BF algebra, namely transitive ideal and we have introduced some theorems and properties that relate to other types of algebras. Also, we define a new type of filters, is called BF filter and tried to study it and linked it to other concepts in BF algebra. Finally, we introduced the pseudo BF-algebra and some concepts and properties that belong to him and then we studied some of the theorems linking the ideals that exist between them.
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