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I am reading "The Basics of Abstract Algebra" by Paul E. Bland ... ...
I am currently focused on Chapter 3: Sets with Two Binary Operations: Rings ... ...
I need help with Bland's proof of the Second Isomorphism Theorem for rings ...
Bland's Second Isomorphism Theorem for rings and its proof read as follows:
View attachment 7969
https://www.physicsforums.com/attachments/7970
In the above proof by Bland we read the following:
" ... ... This map is easily shown to be a well defined ring homomorphism with kernel $$I_1/I_2$$. ... ... "I can see that $$f$$ is a ring homomorphism ... but how do we prove that the kernel is $$I_1/I_2$$ ... ... ?Hope someone can help ...
Peter
I am currently focused on Chapter 3: Sets with Two Binary Operations: Rings ... ...
I need help with Bland's proof of the Second Isomorphism Theorem for rings ...
Bland's Second Isomorphism Theorem for rings and its proof read as follows:
View attachment 7969
https://www.physicsforums.com/attachments/7970
In the above proof by Bland we read the following:
" ... ... This map is easily shown to be a well defined ring homomorphism with kernel $$I_1/I_2$$. ... ... "I can see that $$f$$ is a ring homomorphism ... but how do we prove that the kernel is $$I_1/I_2$$ ... ... ?Hope someone can help ...
Peter