Gcd Modulo a Primary Triangular Set of Dimension Zero

Computing gcd over a triangular set T is the core routine of the machinery of some triangular decomposition methods, in the realm of polynomial ideal theory. As such it has been studied intensively and is well-understood and implemented in several situations, especially in the case where coefficients are over a radical triangular set; It is not the case over a non-radical one. This paper introduces a gcd notion in this case, when additionally for simplicity T is assumed to be primary. It is built upon the Henselian property of the coefficient ring, and is natural in that it is linked with the subresultant sequence of a and b modulo T. A general algorithm still relies on some assumptions, except for the case of a triangular set of one variable.