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The main purpose of this paper is to present a lifting theorem generalizing the well-known Wedderburn᎐Malcev theorem. We then show how this result can be applied to various questions concerning the structure of blocks and source algebras. In particular, we indicate how it can be used to give an alternative proof of Puig's main theorem on nilpotent blocks.In the following, we fix a complete discrete valuation ring R with Ž . algebraically closed residue field F s RrJ R of characteristic p ) 0 and field of fractions K of characteristic 0. For an element ␣ g R, we denote by ␣ its image in F. All our R-algebras will be associative with identity element and finitely generated R-modules. We do not require our R-algebra homomorphisms to be unitary.Let us fix an R-algebra A. Every A-module will be considered as an R-module in the usual way. We will tacitly assume that all our A-bimodules M satisfy rm s mr for r g R, m g M. Then we can regard

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