Abstract
ABSTRACT Let Λ be an Artinian ring and let B be a right projective Λ-Λ-bimodule. Recall that a ring Γ is an extension of Λ by B if we have a short exact sequence of Abelian groups , where f is a homomorphism of rings. Recall that a Λ-module M is called liftable to Γ if there exists a Γ-module X such that X/BX≅ M and Tor Γ n (Λ,X) = 0 for all n > 0. The finitistic dimension of Γ is the supremum of the projective dimensions of finitely generated Γ-modules of finite projective dimension. We study Γ-modules of finite projective dimension and we give upper bounds on the finitistic dimension of Γ in terms of the finitistic dimension of liftable Λ-modules.
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