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A new homological dimension is introduced to measure the quality ofresolutions of `singular' finite dimensional algebras (of infinite globaldimension) by `regular' ones (of finite global dimension). Upper bounds areestablished in terms of extensions and of Hochschild cohomology, and finitenessin general is derived from homological conjectures. Then invariance understable equivalences is shown to hold, with some exceptions when there are nodesin case of additive equivalences, and without exceptions in case oftriangulated equivalences. Stable equivalences of Morita type and derivedequivalences, both between self-injective algebras, are shown to preserverigidity dimension as well.

Rigidity dimension - a homological dimension measuring resolutions of algebras by algebras of finite global dimension