I was doing some self study and have questions:(adsbygoogle = window.adsbygoogle || []).push({});

1. p(x)=x^{7}+11 over Q(a), R.

where a is 7-th root of unity. What are Galouis groups?

For the 1st case I got Z_{7}, second not sure. need hint for that

2. need hint. I know it is easy: M is an R-module. Show that Hom_{R}(R,M)[tex]\cong[/tex]M.

3. Spse that I is an ideal of R such that I^{k}=0 for some k>0 integer. Let M, N be R-modules and let [tex]\phi[/tex]:M->N be an R-module hom. Prove that if induced map [tex]\bar{\phi}[/tex]:M/IM->N/IN is surjective, then [tex]\phi[/tex] is surjective.

4. show that 2[tex]\otimes[/tex]1 [tex]\neq[/tex]0 in 2Z[tex]\otimes[/tex]Z/2Z.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Galous group, modules

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**