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dc.contributor.authorLarone, Jesse
dc.date.accessioned2015-01-05T20:31:11Z
dc.date.available2015-01-05T20:31:11Z
dc.date.issued2015-01-05
dc.identifier.urihttp://hdl.handle.net/10464/5972
dc.description.abstractLet f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].en_US
dc.language.isoengen_US
dc.publisherBrock Universityen_US
dc.subjectPrime polynomialsen_US
dc.subjectPrime rational functionsen_US
dc.subjectCritical Valuesen_US
dc.subjectResultanten_US
dc.subjectIntegral polynomialsen_US
dc.titlePrime Rational Functions and Integral Polynomialsen_US
dc.typeElectronic Thesis or Dissertationen_US
dc.degree.nameM.Sc. Mathematics and Statisticsen_US
dc.degree.levelMastersen_US
dc.contributor.departmentDepartment of Mathematicsen_US
dc.degree.disciplineFaculty of Mathematics and Scienceen_US
dc.embargo.termsNoneen_US
refterms.dateFOA2021-07-31T01:48:49Z


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