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dc.contributor.authorChapman, Adam
dc.date.accessioned2020-10-22T10:45:59Z
dc.date.available2020-10-22T10:45:59Z
dc.date.issued2020-10-22
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3802
dc.description.abstractIn this paper, we prove that given an octonion algebra $A$ over a field $F$, a subring $E \subseteq F$ and an octonion $E$-algebra $R$ inside $A$, the set $S$ of polynomials $f(x) \in A[x]$ satisfying $f(R) \subseteq R$ is an octonion $(S\cap F[x])$-algebra, under the assumption that either $\frac{1}{2} \in R$ or $\operatorname{char}(F) \neq 0$, and $R$ contains the standard generators of $A$ and their inverses. The project was inspired by a question raised by Werner on whether integer-valued octonion polynomials over the reals form a nonassociative ring. We also prove that the polynomials $\frac{1}{p}(x^{p^2}-x)(x^p-x)$ for prime $p$ are integer-valued in the ring of polynomials $A[x]$ over any real nonsplit Cayley-Dickson algebra $A$.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2020-21
dc.subjectAlternative algebrasen_US
dc.subjectOctonion algebrasen_US
dc.subjectRing of polynomialsen_US
dc.subjectInteger-valued polynomialsen_US
dc.subjectCayley-Dickson algebrasen_US
dc.titleOctonion Polynomials with Values in a Subalgebraen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2020-21
local.scientificprogramResearch in Pairs 2020en_US
local.series.idOWP-2020-21en_US
local.subject.msc17en_US
dc.identifier.urnurn:nbn:de:101:1-2020121012125835956735
dc.identifier.ppn1742705405


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