57 583
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 Hym@n B@ss

Question #24894
Show that Nil*R is precisely the set of all strongly nilpotent elements of R.
Expert's answer
First assume a is not in Nil*R.Then there exists an m-system M containing a and notcontaining 0. Take a1 = a, and inductively a_n+1 ∈(a_nRa_n) ∩ M. Then we get a sequence a1, a2,a3, . . . of the desired type which is never 0. Therefore, a isnot strongly nilpotent. Conversely, if a is not strongly nilpotent,there exists a set M = {ai : i ≥ 1} of nonzeroelements such that a1 = a and a_n+1 ∈ a_nRa_n (∀n). Thus, M is an m-system. Since 0 is not in M,then a is not inNil*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