The square of a formal laurent series

R.P.F.
Messages
210
Reaction score
0
Let F be a field. Let c \in F.

I am trying to show that if
c = f^2 where f\in F[[x]], then f\in F.

So I am able to get rid of the terms with negative exponent. So now I'm left with a formal power series. Anyone knows how to do this? Thanks!
 
Physics news on Phys.org
Figured it out. So sorry, guys. :(
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread '##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?'

I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
View full post »

Similar threads

About semidirect product of Lie algebra
Replies
19
Views
3K
I Fundamental theorem of arithmetic from Jordan-Hölder theorem
Replies
5
Views
2K
A Laurent series for algebraic functions
Replies
9
Views
3K
I Question about "A Group Epimorphism is Surjective"
Replies
13
Views
573
I Meaning of "identify" & variations in different math context
Replies
5
Views
499
A Expansion with respect to ##z_1##
Replies
1
Views
1K
I About convergence of complex power series on the circle ##|z - z_0|=r##
Replies
22
Views
3K
I Proving inequality about dimension of quotient vector spaces
Replies
25
Views
3K
MHB Ideals of formal power series ring
Replies
1
Views
3K
I How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?
Replies
48
Views
3K

Hot Threads

Recent Insights

Back
Top