The global dimension gldim(R) is the supremum of projective dimensions over all left R-modules; equivalently the supremum of injective dimensions. Zero iff R is semisimple (Wedderburn), at most one iff R is left hereditary (Dedekind…
The global dimension gldim(R) is the supremum of projective dimensions over all left R-modules; equivalently the supremum of injective dimensions. Zero iff R is semisimple (Wedderburn), at most one iff R is left hereditary (Dedekind…