Title of article :
RINGS WITH A SETWISE POLYNOMIAL-LIKE CONDITION
Author/Authors :
TAVAKOLI, A. islamic azad university - Department of Mathematics, ايران , ABDOLLAHI, A. university of isfahan - Department of Mathematics, اصفهان, ايران , BELL, H. E. Brock University - Department of Mathematics, Canada
Abstract :
Let R be an infinite ring. Here, we prove that if 0R belongs to {x1 x2 · · · xn | x1, x2, . . . , xn element of X} for every infinite subset X of R, then R satisfies the polynomial identity x^n = 0. Also, we prove that if 0R belongs to {x1 x2 · · · xn−xn+1 | x1, x2, . . . , xn, xn+1 element of X} for every infinite subset X of R, then x^n = x, for all x element of R.
Keywords :
Primitive rings , polynomial identities , combinatorial conditions.
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
