Let f(a) = r(n) a^n +... + r(m) a^m and g(a) = r"(s) a^s +...+ r" (q) a^q be in R|a| with m>n, s>q and neither r(m) nor r"(q) equal to 0. Then f(a) g(a) = `r(n+s) a^(n+s) +...`r(m+q) a^(m+q). Notice that `r(m+q) = r(m)r"(q) is not zero, so neither is f(a)g(a), and R|a| is an integral domain. This was an answer from someone else and it totally confused me