Galois theory


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Words related to Galois theory

group theory applied to the solution of algebraic equations

References in periodicals archive ?
As we shall see later, it plays a central role in globalization, Galois theory for partial actions, and partial representations.
In the paper [32] we studied the adjunction between the category of monoids and the category of groups, given by the group completion of a monoid, from the point of view of categorical Galois theory.
Swan, Noether's problem in Galois theory, in Emmy Noether in Bryn Mawr (Bryn Mawr, Pa.
The modern approach to Galois theory is undeniably elegant, says Newman (emeritus psychiatry, U.
This mathematics textbook for graduate students covers the fundamentals of abstract algebra including fields and Galois theory, algebraic number theory, algebraic geometry and groups, rings and modules.
With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors.
Pollack introduces algebraic number theory to readers who are familiar with linear algebra, commutative ring theory, Galois theory, a little abelian groups theory, and elementary number theory up to and including the law of quadratic reciprocity.
The connection between categorical and differential Galois theories established by the author (published in 1989) is extended to the context that includes difference Galois theory.
8] contains three distinct subgroups of index 2, there are three distinct quadratic subextensions in K/Q by Galois theory.
Neumann (mathematics, Queen's College) provides a page-facing dual language presentation and systematic English translation of the published and unpublished writings of nineteenth-century French mathematician Evariste Galois, best known for his work in abstract algebra that laid the groundwork for Galois theory and group theory.
Audin includes exercises and two appendices, the first on what one needs to know about differential Galois theory and algebraic curves, making this a suitable candidate for self-study as well as a classroom text.
After introducing notation and Zorn's lemma, he arranges the problems in chapters on integers and integers mod <n/>, groups, rings, linear algebra and canonical forms of linear transformations, and fields and Galois theory.
It is enough to assume that X is a path-connected, locally path-connected and semilocally simply-connected, to use Galois theory.
Other topics include polynomials, factorization in integral domains, p-groups and the Sylow theorems, Galois theory, and finiteness conditions for rings and modules.
He begins with a discussion of Lie group theory's intellectual underpinnings in Galois theory and concludes with a chapter on the application of Lie group theory to solving differential equations, both subjects that are relatively rare in texts on Lie group theory.