Abstract
Let be a commutative unital Banach algebra with infinite spectrum. Then by Helemskiĭ's global dimension theorem the global homological dimension of is strictly greater than one. This estimate has no analogue for abstract algebras or non-normable topological algebras. It is proved in the present paper that for every unital Banach algebra the global homological dimensions and the homological bidimensions of the Banach algebras and (assuming certain restrictions on ) are related by and . Thus, a partial extension of Helemskiĭ's theorem to tensor products is obtained.Bibliography: 28 titles.
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