Answered: Theorem: Let A and B be R-dibmodules af… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section: Chapter Questions

Problem 20RQ

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Theorem: Let A and B be R-dibmodules af lelt
R-modules M and N respectively. Then,
MXN
AXB
A

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QI) Let f A→B be a module homomorphism and let U be a submodule of A. It is well-know that US f(f(U)). When U = f(f(U))? and why? Q2) State and prove Modular Law. Q3) Show that every vector space over a skew field has a basis. Q4) Draw the lattice of the Z-module and then determine direct summand of this module. Q5) Show that: 30Z (1) Any subset of Qz has more than one element is not free. (2) Qz has no minimal and no maximal submodules. (3) Let a A B and B B Boa is an epimorphism C be homomorphisms. Then, we have ẞ is an epimorphism.
QI) Let f: A B be a module homomorphism and let U be a submodule of A. - It is well-know that US f(f(U)). When U = f(f(U))? and why? Q2) State and prove Modular Law." Q3) Show that every vector space over a skew field has a basis. Q4) Draw the lattice of the Z-module: and then determine direct summand of this module. Q5) Show that: 302 (1) Any subset of Qz has more than one element is not free. (2) Qz has no minimal and no maximal submodules. (3) Let a A B and B : B →C be homomorphisms. Then, we have Boa is an epimorphism: ẞ is an epimorphism.
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