Global Dimension of Polynomial Rings in Partially Commuting Variables

Details Global Dimension of Polynomial Rings in Partially Commuting Variables Global Dimension of Polynomial Rings in Partially Commuting Variables

2008-09-26

arxiv.org/abs/0809.4518v1

Mathematics

Category Theory

11 pages, 2 figures

Scientific paper

10.1007/s00233-010-9264-8

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.

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