Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [52]-53).

For D an integral domain with field of fractions K and E a subset of K, the ring Int (E,D) = {f e K[X]lf (E) C D} of integer-valued polynomials on E has been well studies. In particulare, when E is a finite subset of D, Chapman, Loper, and Smith, as well as Boynton and Klingler, obtained a bound on the number of elements needed to generate a finitely generated ideal of Ing (E, D) in terms of the corresponding bound for D. We obtain analogous results for Int (r) (E, D) - {f e K [X]lf(k) (E) c D for all 0 < k < r} , for finite E and fixed integer r > 1. These results rely on the work of Skolem [23] and Brizolis [7], who found ways to characterize ideals of Int (E, D) from the values of their polynomials at points in D. We obtain similar results for E = D in case D is local, Noetherian, one-dimensional, analytically irreducible, with finite residue field. / by Yuri Villanueva. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

In this dissertation, we consider six Prufer-like conditions on acommutative ring R. These conditions form a hierarchy. Being a Prufer ring is not a local property: a Prufer ring may not remain a Prufer ring when localized at a prime or maximal ideal. We introduce a seventh condition based on this fact and extend the hierarchy. All the conditions of the hierarchy become equivalent in the case of a domain, namely a Prufer domain. We also seek the relationship of the hierarchy with strong Prufer rings. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2015 / FAU Electronic Theses and Dissertations Collection

Seja p um número primo e seja uma raiz p - ésima primitiva da unidade. Considere os seguintes elementos i := 1 + + 2 + ... + i-1 para todo 1 i k do anel Z[] onde k = (p-1)/2. Nesta tese nós descrevemos explicitamente um conjunto gerador para o grupo das unidades do anel de grupo integral ZC2p; representado por U(ZC2p); onde C2p representa o grupo cíclico de ordem 2p e p satisfaz as seguintes condições: S := { -1, , u2, ... uk } gera U(Z[]) e U(Zp) = ou U(Zp)2 = e -1 U(Zp); que são verificadas para p = 7; 11; 13; 19; 23; 29; 53; 59; 61 e 67. Com o intuito de estender tais ideias encontramos um conjunto gerador para U(Z(C2p x C2) e U(Z(C2p x C2 x C2) onde p satisfaz as mesmas condições anteriores acrescidas de uma nova hipótese. Finalmente com o auxílio dos resultados anteriores apresentamos um conjunto gerador das unidades centrais do anel de grupo Z(Cp x Q8); onde Q8 representa o grupo dos quatérnios, ou seja, Q8 := <a; b : a4 = 1; a2 = b2; b-1 a b = a-1 >. / Let p be an odd prime integer, be a pth primitive root of unity, Cn be the cyclic group of order n, and U(ZG) the units of the Integral Group Ring ZG: Consider ui := 1++2 +: : :+i1 for 2 i p + 1 2 : In our study we describe explicitly the generator set of U(ZC2p); where p is such that S := f1; ; u2; : : : ; up1 2 g generates U(Z[]) and U(Zp) is such that U(Zp) = 2 or U(Zp)2 = 2 and 1 =2 U(Zp)2; which occurs for p = 7; 11; 13; 19; 23; 29; 37; 53; 59; 61, and 67: For another values of p we don\'t know if such conditions hold. In addition, under suitable hypotheses, we extend these ideas and build a generator set of U(Z(C2p C2)) and U(Z(C2p C2 C2)): Besides that, using the previous results, we exhibit a generator set for the central units of the group ring Z(Cp Q8) where Q8 represents the quaternion group.

Seja p um número primo e seja uma raiz p - ésima primitiva da unidade. Considere os seguintes elementos i := 1 + + 2 + ... + i-1 para todo 1 i k do anel Z[] onde k = (p-1)/2. Nesta tese nós descrevemos explicitamente um conjunto gerador para o grupo das unidades do anel de grupo integral ZC2p; representado por U(ZC2p); onde C2p representa o grupo cíclico de ordem 2p e p satisfaz as seguintes condições: S := { -1, , u2, ... uk } gera U(Z[]) e U(Zp) = ou U(Zp)2 = e -1 U(Zp); que são verificadas para p = 7; 11; 13; 19; 23; 29; 53; 59; 61 e 67. Com o intuito de estender tais ideias encontramos um conjunto gerador para U(Z(C2p x C2) e U(Z(C2p x C2 x C2) onde p satisfaz as mesmas condições anteriores acrescidas de uma nova hipótese. Finalmente com o auxílio dos resultados anteriores apresentamos um conjunto gerador das unidades centrais do anel de grupo Z(Cp x Q8); onde Q8 representa o grupo dos quatérnios, ou seja, Q8 := <a; b : a4 = 1; a2 = b2; b-1 a b = a-1 >. / Let p be an odd prime integer, be a pth primitive root of unity, Cn be the cyclic group of order n, and U(ZG) the units of the Integral Group Ring ZG: Consider ui := 1++2 +: : :+i1 for 2 i p + 1 2 : In our study we describe explicitly the generator set of U(ZC2p); where p is such that S := f1; ; u2; : : : ; up1 2 g generates U(Z[]) and U(Zp) is such that U(Zp) = 2 or U(Zp)2 = 2 and 1 =2 U(Zp)2; which occurs for p = 7; 11; 13; 19; 23; 29; 37; 53; 59; 61, and 67: For another values of p we don\'t know if such conditions hold. In addition, under suitable hypotheses, we extend these ideas and build a generator set of U(Z(C2p C2)) and U(Z(C2p C2 C2)): Besides that, using the previous results, we exhibit a generator set for the central units of the group ring Z(Cp Q8) where Q8 represents the quaternion group.