The Morita Theorems |
Common terms and phrases
A-A-bimodule A-A-isomorphic A-endomorphism A-homomorphism A-submodules algebraic apply Morita Auslander and Goldman bijection Brauer group category of left category theory central separable K-algebra classes of A-A-progenerators commutative ring Corollary cosets denote direct sum direct summand division ring elements endomorphism epimorphism finitely generated projective g₁f galois group gf is non-zero group of K-automorphisms Hom P,P Homg PB homomorphism Homp P,B Homy M,N ideal in Ae identity functor induces inner automorphisms isomorphism of categories K-Aut K-Aut(M K-categories K-isomorphisms lattice left A-module left isomorphism classes left isomorphism type left multiplication Lemma Let f Mathematics QA 247 module Moreover Morita Context MORITA THEOREMS morphisms natural transformation number field opposite ring progenerator projective K-module Proof proper monomorphism Proposition Center right B-module right multiplication Rosenberg-Zelinski sided ideals simple Artinian ring subgroup sum of copies surjective symmetric u₁ Wedderburn Structure Theory X₁ xu₁ zero