Mixed Newton numbers and isolated complete intersection singularities

Let f:(ⁿ, 0) (^p, 0) be a complete intersection with an isolatedsingularity at the origin. We give a lower bound for the Milnornumber of f in terms of the mixed multiplicities of a set ofmonomial ideals attached to the Newton polyhedra of the componentfunctions of f. The Milnor number of f equals the bound thatwe give when f satisfies a condition that we define and thatextends the notion of Newton non-degenerate function studiedby Kouchnirenko. Our techniques are based on the notion of integralclosure of submodules and its relation with Buchsbaum–Rimmultiplicity and mixed multiplicities of a set of ideals.