On Permutation Commutative Q-Algebras with Their Ideals
Moataz Sajid Sharqi, Shuker Mahmood Khalil · 2023
Some of the new algebraic topics investigated in this paper, like permutation commutative Q-algebra, permutation commutative G-part., permutation commutative p-radical., permutation commutative$\mathbf{p}$-semisimple and permutation commutative Q-ideal are given and studied. We show that if the associative law is held for any permutation commutative Q-algebra$(\boldsymbol{X},\#,\boldsymbol{T})$., then$X$is a group under the operation “$\#\prime\prime$. Also, the left cancellation law holds in$G(X)$., where$\boldsymbol{G}(\boldsymbol{X})$is the permutation commutative G-part of$\boldsymbol{X}$. Additionally, the homomorphism, kernel, and image of permutation commutative Q-algebras and permutation commutative implicative Q-ideals were outlined with particular outcomes linked to the new concepts that we developed and tested.