Several new classes of the algebraic problems are investigated, such as permutation d/d-edge/d-transitive-algebras, permutation d/d#-ideals and permutation d-subalgebras are discussed and looked into. We show that the product for any member in permutation d-algebra from the right with constant is equal the same member. Also, any permutation d-algebra is a permutation d-transitive algebra if and only if its extended edge permutation d-algebra is permutation d-transitive algebra. Additionally, permutation d*-algebra, permutation d-morphism, equivalence relation, congruence class and quotient permutation d-algebras were defined with specific results relating to these new notions are examined.
In this paper, the notion of an entirely novel type of BP-algebras was introduced. Moreover, their fundamental characteristics were examined. Also, we thought about and talked about and talked about some novel ideas in permutation BP-algebras, such as {1}-commutative permutation BP-algebras, and some relationships with permutation BH- algebras and permutation B-algebras.
Some of the novel algebraic topics explored in this paper, like Permutation Q - algebra, permutation G - part, permutation p-radical, permutation p - semisimple and permutation ideal are discussed and looked into. We show that if ( X, #, {1}) is a permutation Q - algebra, then (λiβ # (λiβ # λjβ)) # λjβ = {1}, ∀λiβ, λjβ ∈ X. Also, in the permutation G - part G(X) of X, the left cancellation law is hold and for any β - set λiβ in Permutation Q - algebra (X, #, {1}), we consider that λiβ belongs to G(X). Additionally permutation implicative, homomorphism, kernel and image of permutation Q - algebras were defined with specific results relating to our unique notions have been developed and examined.
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