Suppose that R is a nonzero commutative ring with identity and every submodule of every free R-module

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Suppose that R is a nonzero commutative ring with identity and every submodule of every free R-module is free, then R is a principal ideal domain. we need to show that every ideal of R is generated by a single element.

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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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Suppose that R is a nonzero commutative ring with identity and every submodule of every free R-module

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ANSWER To show that every ideal of R is generated by a single element we need to show that R is a pr...View the full answer

Algebra Graduate Texts In Mathematics 73

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