Let R,S be rings and A R , s B R, s C R, D R (bi)modules

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Let R,S be rings and A_R, s^BR, s^CR, D_R (bi)modules as indicated. Let Hom_R denote all right R-module homomorphisms.

(a) Hom_R(A,B) is a left S-module, with the action of S given by (s∫)(a) = s(∫(a)).

(b) If φ: A → A' is an homomorphism of right R-modules, then the induced map φ̅: Hom_R(A',B) → Hom_R(A,B) is an homomorphism at left S-modules.

(d) If Ψ : D → D' is an homomorphism of right R-modules, then Ψ̅ Hom_R(C,D)- HomR(C,D') is an homomorphism of right S-modules.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 15, 2023 03:04 AM

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Let R,S be rings and A R , s B R, s C R, D R (bi)modules

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a HomRAB is a left Smodule with the action of S gi...View the full answer

Algebra Graduate Texts In Mathematics 73

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