Tag: abstract-algebra
- Group Theory – Counting Homomorphisms from S_n to a p-Group
- Localizing a ring twice
- Abstract Algebra – Example of PID Where SL_n is Not Equal to E_n
- If $N \unlhd G$ has index $n$ in $G$, then $g^n \in N$ for all $g \in G$.
- Which fields are closed with respect to roots of polynomial maps but not algebraically closed
- Noetherian localization of a commutative ring
- Finite extension of a characteristic p field is separable if and only if $E=F(E^p)$
- Let $I$ be an ideal of nilpotent elements. Show that if $a$ maps to a unit in $A/I$, then $a$ is a unit in $A$.
- If $A\subset \Bbb Z$ with $|A| = n$, then there exists $t\in \Bbb Z\setminus p\Bbb Z$ such that $\phi(at/p) \le p^{-1/n}$ for all $a\in A$.
- Why is it called Hilbert’s “basis” theorem?