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f-Algebra, d --Algebra, almost f --Algebra and semiprime f --Algebra is introduced and is worked their relations by Aliprantis and Burkinshaw (2006) . The concepts of homomorphism, isomorphism, automorphism and biortomorphism on Riesz spaces have been defined by mathematicians such as Zaanen, Huijsmans, Boulabiar, Buskes and Triki. f-Algebra on biorthomorphisms is worked by Buskes, Page and Yilmaz (2010) and by Boulabiar and Brahmi (2016) on Riesz Space. The algebraic structure of the biortomorphism space by examining by Boulabiar and Brahmi (2016), for e ∈ X+, ∀x1, x2 ∈ X and f1, f2 ∈ Orth(X,X), (f1 *e f2)(X1,X2) = f1(x1,f2(e,X2)) with the help of the product defined as this space has been shown to have an f-algebra structure. In this study, to examine the relationship between f-Algebra, d-Algebra, almost f-Algebra and semiprime f-Algebra in Orth (X, X) space with the help of multiplication *e and we want to examine whether the transitions between X semiprime f-Algebra and d-Algebra and almost f-Algebra given by the Theorem 1.10 are also provided in algebra types defined on biortomorphisms. We already know that f-algebra on biorthomorphisms in Riesz Space. In this paper, orthomorphisms is introduced on X is denoted Orth (X) and biorthomorphisms is denoted Orth (X,X). [ABSTRACT FROM AUTHOR]