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Showing 1 to 14 of 14 for “"Galois theory"”.
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A Survey of Galois Theory
In this paper, we will see a summary of Galois theory and some results utilized in Algebra. We state and prove the Fundamental Theorem of Galois theory and then work a few examples to show its application to the determination of lattices of groups and fields. In Chapter 2, we prove the theorem …
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Topics in Inverse Galois Theory
Galois theory, the study of the structure and symmetry of a polynomial or associated field extension, is a standard tool for showing the insolvability of a quintic equation by radicals. On the other hand, the Inverse Galois Problem, given a finite group G, find a finite extension of the rational …
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Topics in categorical algebra and Galois theory
… then give a thorough description of categorical Galois theory, which yields an analogue for the fundamental theorem of Galois theory in an abstract category by making use of the notions of admissibility and effective descent. We show that the admissibility of a functor can be extended to the …
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Extensive categories, commutative semirings and Galois theory
We describe the Galois theory of commutative semirings as a Boolean Galois theory in the sense of Carboni and Janelidze. Such a Galois structure then naturally suggests an extension to commutative semirings of the classical theory of quadratic equations over commutative rings. We show, however, …
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On the Inverse Problem in Differential Galois Theory
Differential Galois theory generalizes the usual Galois theory for polynomials to differential equations. There is the notion of a splitting field (Picard-Vessiot extension) of a differential equation, and the differential Galois group is the group of automorphisms of this extension which fix the …
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Iterative Differential Galois Theory in Positive Characteristic: A Model Theoretic Approach
… a natural extension of Kolchin's differential Galois theory to positive characteristic iterative differential fields, generalizing to the non-linear case the iterative Picard-Vessiot theory recently developed by Matzat and van der Put. Instead of taking an algebraic approach, we use the methods …
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Coverings and Descent Theory of Finite Spaces
This thesis presents the categorical Galois theory of the reflection of the category of finite topological spaces into the category of discrete finite topological spaces. This turns out to be nothing but the equivalence between the category of coverings of a connected finite topological space and …
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Calculation of Galois groups
<p>In the 19th Century Galois developed a method for determining whether an equation is solvable. It relied on the close relationship between fields and their automorphism group. This paper is a survey of the techniques of Galois theory. After presenting the main results of elementary Galois theory …
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Arithmetic Differential Subgroups of GL_{n}
A remarkable and special Galois Theory appears from the study of the arithmetic analogue of ordinary differential equations; where functions are replaced by integers, the derivative operator replaced by the Fermat quotient operator' and differential equations are replaced by arithmetic differential …
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A CATEGORICAL-ALGEBRAIC EXPLORATION OF MODELS FOR MANY-VALUED LOGIC
… this pair of subcategories defines a pretorsion theory, which is the generalization to a non-pointed context of the classical notion of torsion theory. We study the Galois structure associated with the reflection of semisimple MV-algebras, proving that it is admissible from the point of view of …
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On Greenberg's question: an algebraic and computational approach
… up into four cases, depending on properties of Galois groups. This analysis is then used to give a positive answer to Greenberg’s question in some nontrivial examples.
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Three viewpoints on semi-abelian homology
… question naturally arises of how the homology theory depends on the chosen comonad. Again it is well-known in the abelian case that the theory only depends on the projective class which the comonad generates. We extend this to the semi-abelian setting by proving a comparison theorem for …
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Primitive near-rings
The theory of near-rings has arisen in a variety of ways. There is a natural desire to generalise the theory of rings and skew fields by relaxing some of their defining axioms. It has also been the hope of some mathematicians that certain problems in group theory, particularly involving permutation …
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Quasicategorical Galois theories
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms