55 641
Assignments Done
97,6%
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 Abstract Algebra Question for Tsit Lam

Question #17655
Show that for any ideal I ⊆ rad R, the natural map GLn(R) → GLn(R/I) is surjective.

Expert's answer
First consider the case n =1. For x ∈ R, we have that x ∈ U(R) iff x ∈ U(R/I). Therefore, U(R)→ U(R/I) is surjective. Applying this to the matrix ring Mn(R)and its ideal Mn(I) ⊆ Mn(rad R) = rad Mn(R),we see that U(Mn(R)) → U(Mn(R)/Mn(I))= U(Mn(R/I)) is onto; that is, GLn(R) → GLn(R/I)is onto.

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