dc.contributor.author | Sodhi, Asmita | |
dc.date.accessioned | 2020-04-14T14:29:44Z | |
dc.date.available | 2020-04-14T14:29:44Z | |
dc.date.issued | 2020-04-14T14:29:44Z | |
dc.identifier.uri | http://hdl.handle.net/10222/78501 | |
dc.description.abstract | A polynomial f(x) in Q[x] is called integer-valued if f(n) is in Z for all n in Z. Bhargava's p-orderings and p-sequences have been helpful tools in the study of integer-valued polynomials over subsets of Z and arbitrary Dedekind domains, and similar
useful definitions exist of nu-orderings and nu-sequences in the case of certain noncommutative rings. In a 2015 paper by Evrard and Johnson, these nu-sequences are used to construct a regular p-local basis for the rational integer-valued polynomials over
the ring of 2x2 integer matrices M_2(Z) by way of moving the problem to maximal orders within an index 2 division algebra over Q_p. In this work, we will demonstrate how the construction used there extends nicely to maximal orders in index p division
algebras over Q_2, where p is an odd prime, thereby giving the construction for a regular basis for polynomials that are integer-valued over this maximal order | en_US |
dc.language.iso | en | en_US |
dc.subject | algebraic number theory | en_US |
dc.subject | integer-valued polynomials | en_US |
dc.subject | division algebras | en_US |
dc.subject | maximal orders | en_US |
dc.subject | polynomials | en_US |
dc.title | Polynomials Integer-Valued on Maximal Orders in Division Algebras | en_US |
dc.date.defence | 2020-03-26 | |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.degree | Doctor of Philosophy | en_US |
dc.contributor.external-examiner | Alan Loper | en_US |
dc.contributor.graduate-coordinator | David Iron | en_US |
dc.contributor.thesis-reader | Karl Dilcher | en_US |
dc.contributor.thesis-reader | Rob Noble | en_US |
dc.contributor.thesis-supervisor | Keith Johnson | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.manuscripts | Not Applicable | en_US |
dc.contributor.copyright-release | Not Applicable | en_US |