57 557
Assignments Done
Successfully Done
In February 2018
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 #17653
For any left artinian ring R with Jacobson radical J, show that
soc(R_R) = {r ∈ R : Jr = 0} and soc(RR) = {r ∈ R : rJ = 0}.
Expert's answer
We use fact: soc(M) ⊆ {m ∈ M : (rad R) · m = 0}, withequality if R/rad R is an artinian ring.
Since R/rad R isartinian, the two desired equations follow by applying mentioned fact (and its
right analogue) to the modules RR and RR.

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!


No comments. Be first!

Leave a comment

Ask Your question