Abstract
Introduction. Epstein [2 ] has published certain results on deficiencies of finite presentations of groups. It is desired here to record analogues of some of those results for finite presentations of linear algebras. For this purpose it is relevant to define a certain homology theory for algebras (§1); thereafter the discussion is closely analogous to that in [2]. A connection between cohomology and a particular homology group related to deficiencies is considered in §3. Finally it is mentioned that these facts have analogues within commutator varieties of groups.
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