Bezoutian and quotient ring structure

In this paper, we present different results related to bezoutian and residue theory. We consider, in particular, the problem of computing the structure of the quotient ring by an affine complete intersection, and an algorithm to obtain it, as conjectured in [Cardinal, J.-P., 1993. Dualité et algorithmesitératifs pour la résolution de systèmespolynomiaux. Ph.D. Thesis, Univ. de Rennes]. We analyze it in detail and prove the validity of the conjecture, for a modification of the initial method. Direct applications of the results in effective algebraic geometry are given.