Global Dimension of Polynomial Rings in Partially Commuting Variables

Abstract

For any free partially commutative monoid $M(E,I)$, we compute the global dimension of the category of $M(E,I)$-objects in an Abelian category with exact coproducts. As a corollary, we generalize Hilbert's Syzygy Theorem to polynomial rings in partially commuting variables.

11 pages, 2 figures

Cited by in corpus (2)

• The Cubical Homology of Trace Monoids
• The Homology Groups of a Partial Trace Monoid Action