55 602
Assignments Done
97,9%
Successfully Done
In November 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Algebra Question for sanches

Question #17277
Show that if f : R → S is a surjective ring homomorphism, then f(rad R) ⊆ rad S.
Give an example to show that f(rad R) may be smaller than rad S.
Expert's answer
The inclusion f(rad R)⊆ rad S is clear since, for any maximal left ideal m of S,the inverse image f−1(m) is a maximal left idealof R. To give an example of strict inclusion, let R = Z and let fbe the natural projection of R onto S = Z/4Z. Here, f(radR) = f(0) = 0, but rad S = 2Z/4Z is nonzero.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question