id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5493	Ansari, Abu Zaid ; Shujat, Faiza; Kamel, Alwaleed; Fallatah, Ahlam	Jordan $\varphi$-centralizers on Semiprime and Involution Rings	2025	10	.pdf	application/pdf	3941	269	80	Throughout, R shall stand for an associative ring with unity e. A ring R is termed as p-torsion free, where p > 1, if pr = 0 entails r = 0 for every r ∈ R. We commence with the equation (1) by replacing r by r + kt, we get the fol- lowing for k being a positive integer and t ∈ R 3H(r3p+ ( 3p 1 ) (r3p−1)kt+ ( 3p 2 ) r3p−2k2t2+ ...+k3pt3p)	cache/ejpam-5493.pdf	txt/ejpam-5493.txt