Galois extensionIn mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed by the automorphism group Aut(E/F) is precisely the base field F. The significance of being a Galois extension is that the extension has a Galois group and obeys the fundamental theorem of Galois theory. A result of Emil Artin allows one to construct Galois extensions as follows: If E is a given field, and G is a finite group of automorphisms of E with fixed field F, then E/F is a Galois extension.
Economic rentIn neoclassical economics, economic rent is any payment (in the context of a market transaction) to the owner of a factor of production in excess of the cost needed to bring that factor into production. In classical economics, economic rent is any payment made (including imputed value) or benefit received for non-produced inputs such as location (land) and for assets formed by creating official privilege over natural opportunities (e.g., patents).
Rent-seekingRent-seeking is the act of growing one's existing wealth by manipulating the social or political environment without creating new wealth. Rent-seeking activities have negative effects on the rest of society. They result in reduced economic efficiency through misallocation of resources, reduced wealth creation, lost government revenue, heightened income inequality, risk of growing political bribery, and potential national decline.
Galois theoryIn mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler and easier to understand. Galois introduced the subject for studying roots of polynomials.
Field extensionIn mathematics, particularly in algebra, a field extension is a pair of fields such that the operations of K are those of L restricted to K. In this case, L is an extension field of K and K is a subfield of L. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers. Field extensions are fundamental in algebraic number theory, and in the study of polynomial roots through Galois theory, and are widely used in algebraic geometry.
