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### Let A be an Artin algebra, let M be a generator-cogenerator for A- mod, and let s be a positive integer. Then: (1) If αi : Vi −→ Mi is a left almost split morphism in

The latter was implicitly designed for applications in class field theory and algebraic number theory, as a group theoretic translation of the class extension homomorphism and the closely related principalization problem, originally… For example, is there an analogue of Artin-Wedderburn for semisimple algebra objects in fusion categories?" ---Artin-Wedderburn in fusion categories

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Algebra ofa magma, a monoid, a group . Definition of an algebra by generators and relations. 9 . Graded subalgebras, graded ideals of a graded algebra . . 3 . almost immediately afterwards E. Artin (always with reference to questions.