Answered: Let R be a ring and M be an R-module,…

Let R be a ring and M be an R-module, and let A and B be submodules of M. Then, a) A+B is a submodule of M. b) A x B is a submodule of M x M. c) Both a and b d) Neither a nor b a) b) d)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.2: Complex Numbers And Quaternions

Problem 47E

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Question

Let R be a ring and M be an R-module, and let A and B be submodules of M. Then,
a) A +B is a submodule of M.
b) A x B is a submodule of M x M.
c) Both a and b
d) Neither a nor b
a)
b)
d)

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