Aspects of order, relative primeness and quotient ring structure for polynomials over integer rings

dc.contributor.author	Walshe, Bridget Anne	en_US
dc.date.accessioned	2024-08-15T20:13:14Z
dc.date.available	2024-08-15T20:13:14Z
dc.date.copyright	2001	en_US
dc.date.issued	2001
dc.degree.department	Department of Mathematics and Statistics	en_US
dc.degree.level	Master of Science M.Sc.	en
dc.description.abstract	Many aspects of polynomials over finite fields have been studied. In this thesis we prove results for polynomials over integer rings that are analogous to known results regarding polynomials over finite fields. A definition of relatively prime for two polynomials over an integer ring is given. Linear algebra and the theory of resultants are used to give two proofs for necessary and sufficient conditions for two polynomials to be relatively prime over certain integer rings We then examine the quotient ring formed by the ring of polynomials over an integer ring mod a monic polynomial f. The existence of an order for certain polynomials over the integers mod n is exhibited and a bound is given for the maximum order of polynomials over the integers mod 2k. Finally, we prove theorems that can be used to simplify the calculation of the order of particular polynomials.
dc.format.extent	55 pages
dc.identifier.uri	https://hdl.handle.net/1828/20034
dc.rights	Available to the World Wide Web	en_US
dc.title	Aspects of order, relative primeness and quotient ring structure for polynomials over integer rings	en_US
dc.type	Thesis	en_US

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