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Results tagged with ac.commutative-algebra
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user 9672
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
6
votes
Accepted
checking if F[x]/I is isomorphic to F[x]/J
If $F$ is finite, $p$ and $q$ are irreducible, and have the same dagree $d$, then $F[x]/I$ and $F[x]/J$ are isomorphic $F$-algebras, since there is (up to isomorphism) only one extension field of a fi …
- 5,654
3
votes
Accepted
Orbits in commutative groups.
The abelian group in question is the product of its Sylow-$p$ subgroups, which are preserved by automorphisms. Therefore the orbits in it are the products of orbits in the Sylow $p$-subgroups. Therefo …
- 5,654
19
votes
Accepted
Is a matrix similar to its transpose over $\mathbb{Z}_p$?
No for $n\geq 3$.
If $A\in M_n(\mathbf Z_p)$ were similar to $A^T\in M_n(\mathbf Z_p)$, then going modulo $p^2$, its image in $M_n(\mathbf Z/p^2\mathbf Z)$ would be similar to the image of its transp …
- 5,654