On permutation G-part in permutation Q-algebras

Abstract

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.