The Łojasiewicz exponent over a field of arbitrary characteristic (Q2348352)

Using generalized power series and Newton's polygon method, the authors extend the notion of the local Łojasiewicz exponent as well as the Łojasiewicz exponent at infinity from \(\mathbb{C}\) to an algebraically closed field \(K\) of elements \(F=(f_1,\dots,f_m)\in K[[X,Y]]^m\) and \(F=(f_1,\dots,f_m)\in K[X,Y]^m\) respectively. They also study the basic properties of these two numbers.