Depth and Stanley Depth of the Canonical Form of a factor of monomial ideals

Abstract

We introduce a so called canonical form of a factor of two monomial ideals. The depth and the Stanley depth of such a factor is invariant under taking the canonical form. This can be seen using a result of Okazaki and Yanagawa [7]. In the case of depth we present in this paper a different proof. It follows easily that the Stanley Conjecture holds for the factor if and only if it holds for its canonical form. In particular, we construct an algorithm which simplifies the depth computation and using the canonical form we massively reduce the run time for the sdepth computation.