The arithmetical rank of k-complete ideals

Abstract

We introduce the notions of algebraic and arithmetic derivation. As an application, we use the combinatorial decomposition of an ideal to provide a constructive method to find the algebraic invariants, as the arithmetical rank,  for a family of squarefree monomial ideals, the $k$--complete ideals $I_k^n,$ also known as squarefree Veronese ideals of degree $k$.