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University of Arizona

1. ACOSTA DE OROZCO, MARIA TEODORA. FIELDS DEFINED BY RADICALS: THEIR TORSION GROUP AND THEIR LATTICE OF SUBFIELDS.

Degree: 1987, University of Arizona

URL: http://hdl.handle.net/10150/184040

Let L/F be a finite separable extension. L* = L{0}, and T(L*/F*) be the torsion subgroup of L*/F*. We explicitly determined T(L*/F*) when L/F is an abelian extension. This information is used to study the structure of T(L*/F*). In particular T(F(α)*/F*) when αᵐ = a ∈ F is explicitly determined. Let Xᵐ - a be irreducible over F with char F χ m and let α be a root of Xᵐ - a. We study the lattice of subfields of F(α)/F and to this end C(F(α)/F,k) is defined to be the number of subfields of F(α) of degree k over F. C(f(α)/F,pⁿ) is explicitly determined for p a prime and the following structure theorem for the lattice of subfields is proved. Let N be the maximal normal subfield of F(α) and set n = [N:F], then C(F(α)/F,k) = C(F(α)/F,(k,n)) = C(N/F,(k,n)). The irreducible binomials X⁸ - b, X⁸ - c are said be equivalent if there exist roots β⁸ = b, γ⁸ = c that F(β) = F(γ). All the mutually inequivalent binomials which have roots in F(α) are determined. These results are applied the study of normal binomials and those irreducible binomials X²ᵉ - a which are normal over F(charF ≠ 2) together their Galois groups are characterized. We finished by considering the radical extension F(α)/F, αᵐ ∈ F, where the binominal Xᵐ - αᵐ is not necessarily irreducible. We see that in the case not every subfield of F(α)/F is the compositum of subfields of prime power order. We determine some conditions such that if F ⊆ H ⊆ F(α) with [H:F] = pᵘq, p a prime, (p,q) = 1, then there exists a subfield F ⊆ R ⊆ H where [R:F] = pᵘ.
*Advisors/Committee Members: Velez, William Yslas (advisor).*

Subjects/Keywords: Torsion theory (Algebra); Lattice theory.

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APA (6^{th} Edition):

ACOSTA DE OROZCO, M. T. (1987). FIELDS DEFINED BY RADICALS: THEIR TORSION GROUP AND THEIR LATTICE OF SUBFIELDS. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/184040

Chicago Manual of Style (16^{th} Edition):

ACOSTA DE OROZCO, MARIA TEODORA. “FIELDS DEFINED BY RADICALS: THEIR TORSION GROUP AND THEIR LATTICE OF SUBFIELDS. ” 1987. Doctoral Dissertation, University of Arizona. Accessed January 21, 2021. http://hdl.handle.net/10150/184040.

MLA Handbook (7^{th} Edition):

ACOSTA DE OROZCO, MARIA TEODORA. “FIELDS DEFINED BY RADICALS: THEIR TORSION GROUP AND THEIR LATTICE OF SUBFIELDS. ” 1987. Web. 21 Jan 2021.

Vancouver:

ACOSTA DE OROZCO MT. FIELDS DEFINED BY RADICALS: THEIR TORSION GROUP AND THEIR LATTICE OF SUBFIELDS. [Internet] [Doctoral dissertation]. University of Arizona; 1987. [cited 2021 Jan 21]. Available from: http://hdl.handle.net/10150/184040.

Council of Science Editors:

ACOSTA DE OROZCO MT. FIELDS DEFINED BY RADICALS: THEIR TORSION GROUP AND THEIR LATTICE OF SUBFIELDS. [Doctoral Dissertation]. University of Arizona; 1987. Available from: http://hdl.handle.net/10150/184040