The projective dimension pd_R(M) of a left R-module M is the minimal length of a projective resolution, or ∞ if no finite one exists. Equivalent characterisations: Ext^{n+1}_R(M, −) = 0, and n-th syzygy is projective. Example: over a…
The projective dimension pd_R(M) of a left R-module M is the minimal length of a projective resolution, or ∞ if no finite one exists. Equivalent characterisations: Ext^{n+1}_R(M, −) = 0, and n-th syzygy is projective. Example: over a…