76 974
Assignments Done
Successfully Done
In June 2019

Answer to Question #24884 in Abstract Algebra for john.george.milnor

Question #24884
Let N1(R) be the sum of all nilpotent ideals in a ring R. If N1(R) is nilpotent, show that N1(R) = Nil*R.
Expert's answer
Let N = N1(R).Say Nn = 0. Then R/N has no nonzero nilpotent ideals. (For, if I/Nis a nilpotent ideal of R/N, then Im ⊆ N for some m, and hence Imn ⊆ Nn = 0. This implies that I ⊆ N.) Therefore, N is semiprime, so N =Nil*R.

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

Privacy policy Terms and Conditions