62 448
Assignments Done
99,2%
Successfully Done
In June 2018

Answer to Question #24889 in Abstract Algebra for Melvin Henriksen

Question #24889
Let I be a left ideal in a ring R such that, for some integer n, an = 0 for all a ∈ I.
Show that I contains a nonzero nilpotent left ideal, and R has a nonzero nilpotent ideal.
Expert's answer
We may assume n is chosenminimal. Since I <> 0, n ≥ 2. Fix an element a I with an−1 <>0. Then an−1Ran−1 =0, so (Ran−1R)2 = 0. Therefore Ran−1Ris a nonzero nilpotent ideal, and I contains the nonzero nilpotentleft ideal Ran−1.

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

Submit
Privacy policy Terms and Conditions