Necessary conditions for irreducibility of algebroid plane curves

Abstract

Let K be an algebraically closed field of characteristic 0 and let ƒ ϵ K[[X]] [Y] be monic. Using the properties of approximate roots given in [J. Algebra 343 (2011), pp. 143-159] we propose some necessary conditions for irreducibility of ƒ in K[[X]] [Y]. The result is expressed only in terms of intersection multiplicities of ƒ with its approximate roots.