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Results tagged with polynomials
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user 17734
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.
6
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answers
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Kernel of evaluation map into field of quotients
Let $R$ be an integral domain and for $a \in R$ denote by $\text{eval}_a: R[X] \to R$ evaluation at $a$. It's well-known (and easy to see) that
$$\ker(\text{eval}_a)=(X-a).$$
The next more complicate …
- 2,019
4
votes
Accepted
Is the restriction of a graded automorphism of a polynomial ring to a polynomial subring lin...
No. Counterexample: Let $\deg x = \deg y = 1$ and take
$$A=\mathbb{F}_2[x,y],\,\,\,B=\mathbb{F}_2[x,y^2],\,\,\,\,\,g(x)=x,\,\,g(y)=x+y$$
As already observed by the OP, since the generators of $B$ hav …
- 2,019