Introduction. By the content of a polynomial with coefficients in a ring R, one understands either the R-ideal or (better) the additive group which the coefficients generate. There are important connexions between the contents of two polynomials and the content of their product, and results of this kind are to be found in the work of Gauss. Here we shall give a wide generalization of a theorem of this type not involving polynomials at all; however, as the reader will observe, the proof is essentially a reduction to the polynomial case.