A ring R is subdirectly irreducible if the intersection of all nonzero ideals of R is nonzero.

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(a) R is subdirectly irreducible if and only if whenever R is isomorphic to a subdirect product of {R_i Ii ϵ I}, R ≅ R_i for some i ε I.

(b) Every ring is isomorphic to a subdirect product of a family of subdirectly irreducible rings.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Aug 18, 2023 05:55 AM

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A ring R is subdirectly irreducible if the intersection of all nonzero ideals of R is nonzero.

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Algebra Graduate Texts In Mathematics 73

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