If R has an identity, then a nonzero unitary R-module A is simple if its only submodules

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If R has an identity, then a nonzero unitary R-module A is simple if its only submodules are O and A. (a) Every simple R-module is cyclic. (b) If A is simple every R-module endomorphism is either the zero map or an isomorphism.

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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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{a) If R has an identity and A is an R-module, then there are submodules Band C of A such that B is unitary, RC = 0 and A = B C. (b) Let A 1 be another R-module, with A 1 = B 1 C1 (B1 unitary, RC 1...
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If R has an identity, then a nonzero unitary R-module A is simple if its only submodules

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a Let A be a simple Rmodule and let a be a nonzero element of A Then th...View the full answer

Algebra Graduate Texts In Mathematics 73

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