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 Post subject: working with submodules
PostPosted: Wed Nov 28, 2018 6:52 pm 

Joined: Fri Jun 24, 2011 10:10 am
Posts: 10
Hi
I have a Question

Let $R$ be the local ring of convergent power series in $n$ variables with
complex coefficients. Denote by $m$ the maximal ideal in $R$, and by
$M$ an $R$-module of finite type.
Consider the sequence of submodules $M_k=m^kM$ in $M$, for $k$ a non-negative integer.
How to compute the codimension of $M_{k+1}$ in $M_k$ ?

Thanks in advance


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