algebraic subfield

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• Algebraic enumeration — is a subfield of enumeration that deals with counting algebraic objects. Algebraic properties and symmetries of the objects being counted can be taken advantage of to simplify the counting process …   Wikipedia

• Algebraic element — In mathematics, the roots of polynomials are in abstract algebra called algebraic elements. They can be created in a larger structure ( adjoined ), not simply found to exist in a given one. More precisely, if L is a field extension of K then an… …   Wikipedia

• Algebraic independence — In abstract algebra, a subset S of a field L is algebraically independent over a subfield K if the elements of S do not satisfy any non trivial polynomial equation with coefficients in K . This means that for every finite sequence α1, ..., α n of …   Wikipedia

• algebraic number theory — noun The subfield of number theory where algebraic numbers are studied using algebra …   Wiktionary

• Abstract algebraic logic — In mathematical logic, abstract algebraic logic (AAL) studies the ways in which classes of algebras may be associated with logical systems, and how these classes of algebras interact with logical systems.OverviewThe archetypal association of this …   Wikipedia

• Motive (algebraic geometry) — For other uses, see Motive (disambiguation). In algebraic geometry, a motive (or sometimes motif, following French usage) denotes some essential part of an algebraic variety . To date, pure motives have been defined, while conjectural mixed… …   Wikipedia

• Gonality of an algebraic curve — In mathematics, the gonality of an algebraic curve C is defined as the lowest degree of a rational map from C to the projective line, which is not constant. In more algebraic terms, if C is defined over the field K and K ( C ) denotes the… …   Wikipedia

• Symmetric product of an algebraic curve — In mathematics, the n fold symmetric product of an algebraic curve C is the quotient space of the n fold cartesian product: C times; C times; ... times; C or C n by the group action of the symmetric group on n letters permuting the factors. It… …   Wikipedia

• Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia

• Glossary of field theory — Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) Definition of a field A field is a commutative ring… …   Wikipedia

• Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… …   Wikipedia