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Apr
28
comment Endomorphisms of a ring $R$ considered as $R$-module
@BrettFrankel Thanks. Looks like I was trying to make things much too complicated.
Apr
28
comment Endomorphisms of a ring $R$ considered as $R$-module
So if $\varphi(1)=v$, then $\varphi(x)=vx$ for every $x\in V$. Then my answer is there is a homomorphism $\varphi_v$ that sends $x\leadsto xv$ for each $v\in V$. Is that right?
Apr
28
asked Endomorphisms of a ring $R$ considered as $R$-module
Apr
22
accepted Determine all automorphisms of $\mathbb{Q}(\sqrt[3]{2},\omega)$
Apr
11
comment Determine all automorphisms of $\mathbb{Q}(\sqrt[3]{2},\omega)$
So, if I'm understanding correctly, if you have irreducible polys for each of the generators individually, then the number of automorphisms is product of what you get when you consider each poly on it's own. Is that right? What's concerning me here is Chris's phrase "at most".
Apr
11
comment Determine all automorphisms of $\mathbb{Q}(\sqrt[3]{2},\omega)$
@lhf: just added homework tag. Thanks
Apr
11
revised Determine all automorphisms of $\mathbb{Q}(\sqrt[3]{2},\omega)$
added homework tag
Apr
11
asked Determine all automorphisms of $\mathbb{Q}(\sqrt[3]{2},\omega)$
Apr
11
accepted Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
Apr
2
asked Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.