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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: 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.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 71E
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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.
Transcribed Image Text: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.
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