Linear generalized polynomials with finiteness conditions

Let R be a semiprime algebra over a field F, and let I be either an ideal of R or a right ideal with zero left annihilator in R. Let B-1 = {Sigma(i=1)(n) a(i)xb(i) \ x is an element of I} and B-2 = {Sigma(i=1)(n) b(i)xa(i) \ x is an element of I}, where a(i), b(i) is an element of R. Suppose that dim B-F(1) < infinity (\B-1\ < infinity). Then dim B-F(2) < infinity and dim B-F(1) = dim B-F(2) (resp. \B-2\ < infinity and \B-1\ = \B-2\).