To coordinate, intelligent agents might need to know something about each other, and about themselves, and about how others view themselves, and how they view others, and how they think others view others, and so on. Taken to an extreme, the amount of knowledge an agent might possess to help make sense of an interaction might outstrip the agent’s limited reasoning capacity (its available time, ...

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 $xin r$.