dc.contributor.author Chapman, Adam dc.date.accessioned 2020-10-22T10:45:59Z dc.date.available 2020-10-22T10:45:59Z dc.date.issued 2020-10-22 dc.identifier.uri http://publications.mfo.de/handle/mfo/3802 dc.description.abstract In 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. en_US 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 $A$. dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2020-21 dc.subject Alternative algebras en_US dc.subject Octonion algebras en_US dc.subject Ring of polynomials en_US dc.subject Integer-valued polynomials en_US dc.subject Cayley-Dickson algebras en_US dc.title Octonion Polynomials with Values in a Subalgebra en_US dc.type Preprint en_US dc.rights.license Dieses 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.license This 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.doi 10.14760/OWP-2020-21 local.scientificprogram Research in Pairs 2020 en_US local.series.id OWP-2020-21 en_US local.subject.msc 17 en_US dc.identifier.urn urn:nbn:de:101:1-2020121012125835956735 dc.identifier.ppn 1742705405
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