The global dimension of a trace monoid ring

Ahmet A. Husainov
2010 Semigroup Forum  
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.
doi:10.1007/s00233-010-9264-8 fatcat:n2xnw2paufdt3g5p5nwzdxcgym