In this paper, some types of a psҽuԁo ℬℋ-algebras arҽ defined. Also, the notions of a psҽudo completely closed ideal, a pseudo strong ideal, a pseudo pideal and a psҽudo qideal are investigated. Also, some properties and relationship among them are discussed.

This paper introduces a new notion of algebra called BS-algebra and some of its properties are discussed in detail. Also, we define a S(a,b) of BS-algebra and discus of properties and theorems of it. Some of theorems of a new ideals of BS-algebra are introduced and proved. Also, we introduced some new types of ideals of Z-algebra and we linked these ideals with some theorems and properties. Also, we define the concept of pseudo Z-algebra and introduced some examples and new concepts in it, including the concept of pseudo b-subalgebra and introduced some theorems and properties in this new concepts.

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