Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am trying to understand the proof of this fact. On page 183, Eisenbud defines a map from the formal power series ring $S[[x_1,x_2,...,x_n]]$ to $R/m^i$ where $R=S[x_1,x_2,...,x_n]$ sending $f$ to $f+m^i$. I have trouble understanding this map since, $f$ need not be an element of $R$ and so what does the coset $f+m^i$ mean? Thanks for any help.

share|cite|improve this question
3  
Pick the series $f$ and just drop all terms of degree larger that $i$. That is a polynomial, the image under Eisenbud's map. – Mariano Suárez-Alvarez Feb 1 '11 at 2:26
    
Thanks. Seems like a strange notation. – Dev Bappa Feb 1 '11 at 23:20
    
it is simple! all monomials of degree >=i lies in m^i – user20970 Dec 10 '11 at 10:40

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.