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inductive and projective limit

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inductive and projective limit

Hello everybody : :-)
I have some exercices to solve, but i don't know how to do them alone :
ex 1: What is the projective limit ( in the category of groups for example ) fr the system $(A_n)_{n\in N}$ with $A_n=\Z[x]/(x^{n+1})$, $f_{n+p,n}:A_{n} \to A_{n+p}$ the multiplication by $x^p$ ?

ex 2: What the inductive limit ( always in the category of groups of course ) for the system $(B_n)_{n\in N}$ with $B = \Z[x]$, $f_{n,n+p}:B_{n} \to B_{n+p}$ the multiplication by $x^p$ ?

Thanks for helping ! :-)


this is just for testing,better to post this somewhere else to get an answer...

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