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Results tagged with polynomials
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user 14639
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.
15
votes
1
answer
588
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Is the ring of quaternionic polynomials factorial?
Two polynomials $P,Q\in \mathbb{H}[x_1,\dots,x_n]$ are similar, if $P=a Q b$ for some $a,b\in \mathbb{H}$. … Struppa, On the Multiplicity of Zeroes of Polynomials with Quaternionic Coefficients, Milan J. Math. 76 (2008), 15-25, DOI 10.1007/s00032-008-0093-0. …
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16
votes
Accepted
Is the ring of quaternionic polynomials factorial?
Just to remove the question from the 'Unanswered' list:
$(x-i)\cdot((x+i)(y+j)+1)=((y+j)(x+i)+1)\cdot(x-i)$, hence $\mathbb{H}[x,y]$ is not factorial.
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