We prove the conjecture of Chen, Wang and Liu in [8] concerning how to calculate the parameter values corresponding to all the singularities, including the infinitely near singularities, of rational planar curves from the Smith normal forms of certain Bezout resultant matrices derived from μ-bases.

Based on the Bezout approach we propose a simple algorithm to determine gcd of two polynomials that don't need division, like Euclidean algorithm, or determinant calculations, Sylvester matrix algorithm. The needs only n steps for degree n. Formal manipulations give discriminant resultant any without needing division calculation.

Based on the Bezout approach we propose a simple algorithm to determine gcd of two polynomials which doesn’t need division, like Euclidean algorithm, or determinant calculations, Sylvester matrix algorithm. The needs only n steps for degree n. Formal manipulations give discriminant resultant any without needing division nor calculation.

in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.