The following conditions on a ring R [with identity] are equivalent: (a) Every [unitary] R-module is projective.

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The following conditions on a ring R [with identity] are equivalent:

(a) Every [unitary] R-module is projective.

(b) Every short exact sequence of [unitary] R-modules is split exact.

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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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The following conditions on a ring R [with identity] are equivalent: (a) Every [unitary] R-module is projective.

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ANSWER To start lets define some terms A module M is projective if every short exact sequence 0 A B ...View the full answer

Algebra Graduate Texts In Mathematics 73

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