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Abstract

This paper contributes to the theory of soft sets. It investigates soft permutation commutative Q-algebras and their applications.A new method of combining permutation sets with soft sets is utilized to investigate new classes of algebra,includingsoft permutation commutative Q-algebra, soft permutation commutative G-part, and soft permutation commutative p-semisimple. This study elucidates an approach to find arelationship between the chemical structure of the atoms for some elements, like silveratom,sodium atom, and chlorine atomand some of our ideas presented here. Furthermore,we demonstratethat if (N,M)is a soft permutation commutative Q-algebra of (��,×,��)and the associative law is held for any ������,������,������∈��(������), then (��(������),×)is a group,∀������∈��. Also, if (��,��)is a soft permutation commutative G-part of ��. Then the left cancellation law is held for any equation ������×��(������)=������×��(������), where ������,������∈��. Next, we prove that if T×N(λiβ)∈G(N,M).Then λiβ∈G(N,M),Also, we show that λjβ∈B(N,M)if and only if (λiβ×N(λjβ))×λiβ=T, where B(N,M)={λiβ∈M|T×N(λiβ)=T}.Subsequently, the cases of orders of (X,×,T)are discussed.Moreover,precise outcomes relating to our new conceptsas well

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