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Results tagged with polynomials
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user 23950
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
5
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1
answer
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Macaulay's example of prime ideals in $\mathbb C[X_1,X_2,X_3]$ having large number of genera...
There is a famous example of Macaulay which shows that there are prime ideals of height two in $\mathbb C[X_1,X_2,X_3]$ having at least $l$ generators for any $l\ge 3$.
In Macaulay's words, the exam …
- 1,313
2
votes
Accepted
Prime ideal ramified in extension if and only if certain polynomial divides another one?
Set $A=k[T,\sqrt f]$. In fact, $A=k[T,U]/(U^2-f)$.
Then $A/gA\simeq k[T,U]/(g,U^2-f)$. If we set $L=k[T]/(g)$, then $A/gA\simeq L[U]/(U^2-\bar f)$.
If $g$ ramifies in $A$ then there is $h\in k[T]$ suc …
- 1,313