Let K be a division ring with center k. For any a ∈ K\k, show that the ideal generated by x − a in K[x] is the unit ideal.
1
Expert's answer
2012-10-17T09:25:58-0400
Fix b ∈ K such that ab (not equal) ba. Then (x − a) (the ideal generated by x − a) contains b(x − a) − (x − a)b = ab − ba ∈U(K), so (x − a) = R.
Numbers and figures are an essential part of our world, necessary for almost everything we do every day. As important…
APPROVED BY CLIENTS
Finding a professional expert in "partial differential equations" in the advanced level is difficult.
You can find this expert in "Assignmentexpert.com" with confidence.
Exceptional experts! I appreciate your help. God bless you!
Comments
Leave a comment