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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.

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)
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