Aristov, O. Yu. The global dimension theorem for non-unital and certain other separable \(C^*\)-algebras. (English. Russian original) Zbl 0863.46033 Sb. Math. 186, No. 9, 1223-1239 (1995); translation from Mat. Sb. 186, No. 9, 3-18 (1995). Summary: We prove that the global homological dimension of a separable \(C^*\)-algebra containing a bi-ideal of finite codimension that cannot be complemented as a subalgebra is at least 2. As a consequence we also obtain this bound for the global dimension of separable \(C^*\)-algebras without an identity and for finite-dimensional separable GCR-algebras. Cited in 1 ReviewCited in 3 Documents MSC: 46H20 Structure, classification of topological algebras 46L05 General theory of \(C^*\)-algebras 46M40 Inductive and projective limits in functional analysis 18G20 Homological dimension (category-theoretic aspects) Keywords:cohomology theory of Banach algebras; global homological dimension; separable \(C^*\)-algebra; bi-ideal of finite codimension PDFBibTeX XMLCite \textit{O. Yu. Aristov}, Sb. Math. 186, No. 9, 1223--1239 (1995; Zbl 0863.46033); translation from Mat. Sb. 186, No. 9, 3--18 (1995) Full Text: DOI