Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.
Tavakoli, A., Abdollahi, A. & Bell, H. E. (2012). Rings with a setwise polynomial-like condition. Bulletin of the Iranian Mathematical Society, 38(2), 305-311.
MLA
Tavakoli, A., Abdollahi, A., & Bell, H. E. "Rings with a setwise polynomial-like condition", Bulletin of the Iranian Mathematical Society, 38, 2, 2012, 305-311.
HARVARD
Tavakoli A., Abdollahi A., Bell H. E. (2012). 'Rings with a setwise polynomial-like condition', Bulletin of the Iranian Mathematical Society, 38(2), pp. 305-311.
CHICAGO
A. Tavakoli, A. Abdollahi & H. E. Bell, "Rings with a setwise polynomial-like condition," Bulletin of the Iranian Mathematical Society, 38 2 (2012): 305-311,
VANCOUVER
Tavakoli A., Abdollahi A., Bell H. E. Rings with a setwise polynomial-like condition. BIMS. 2012;38(2):305-311.
