Tag: abstract-algebra
- 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?
- Is the splitting field of $x^3+2x^2-x-3$ a totally ramified extension of $\mathbb Q_5$
- Does $x^2+y^2=-1$ have solution in $p$ adic number field
- Integral domains with isomorphic field of fractions
- Kernel of morphism of graded modules is graded submodule
- The coset/quotient space of a normal subgroup of a topological group is a topological group
- Jordan-Chevalley decomposition of Lie algebra elements