An elementary proof of Barnettʹs theorem about the greatest common divisor of several univarlate polynomials Original Research Article

This articule provides a new proof of Barnettʹs theorem giving the degree of the greatest common divisor of several univariate polynomials with coefficients in a field in terms of the rank of a well-defined matrix. The new proof is elementary and self-contained (no use of Jordan form or invariant factors), and it is based on some easy to state properties of subresultants. Moreover this proof allows one to generalize Barnettʹs results to the case when the considered polynomials have their coefficients in an integral domain.