Please help me with a solution, not an explanation or definitions. Rather, I want acceptable proof for the test, and I hope to get a solution written on paper and not printed. atanBOREN. Let a: A → B be a homomorphism and let : A→C beepimorphism with Ker()→ Ker(a). Then there exists a homomorphismA:C-B with(1) α α = λφ.(2) Im(A) Im(a).(3) A is a monomorphism Ker() = Ker(a)Remark means that the diagramCαAB

Step 1: Given information,It is a homomorphism…

at an BOREN. Let a: A → B be a homomorphism and let : A→C be epimorphism with Ker()→ Ker(a). Then there exists a homomorphism A:C-B with (1) α α = λφ. (2) Im(A) Im(a). (3) A is a monomorphism Ker() = Ker(a) Remark means that the diagram C α A B

at an BOREN. Let a: A → B be a homomorphism and let : A→C be epimorphism with Ker()→ Ker(a). Then there exists a homomorphism A:C-B with (1) α α = λφ. (2) Im(A) Im(a). (3) A is a monomorphism Ker() = Ker(a) Remark means that the diagram C α A B

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 11E: 11. Show that defined by is not a homomorphism.

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Question

Please help me with a solution, not an explanation or definitions. Rather, I want acceptable proof for the test, and I hope to get a solution written on paper and not printed.

at
an
BOREN. Let a: A → B be a homomorphism and let : A→C be
epimorphism with Ker()→ Ker(a). Then there exists a homomorphism
A:C-B with
(1) α α = λφ.
(2) Im(A) Im(a).
(3) A is a monomorphism Ker() = Ker(a)
Remark means that the diagram
C
α
A
B

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