algebraically closed expansion

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• Puiseux expansion — In mathematics, a Puiseux expansion is a formal power series expansion of an algebraic function. Puiseux s theorem is a classical existence theorem for such an expansion, in the case of one variable.If K is an algebraically closed field of… …   Wikipedia

• Polynomial ring — In mathematics, especially in the field of abstract algebra, a polynomial ring is a ring formed from the set of polynomials in one or more variables with coefficients in another ring. Polynomial rings have influenced much of mathematics, from the …   Wikipedia

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• P-adic number — In mathematics, the p adic number systems were first described by Kurt Hensel in 1897 [cite journal | last = Hensel | first = Kurt | title = Über eine neue Begründung der Theorie der algebraischen Zahlen | journal =… …   Wikipedia

• Algebraic closure — In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics.Using Zorn s lemma, it can be shown that every field has an… …   Wikipedia

• Algebraic geometry and analytic geometry — In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally… …   Wikipedia

• Model theory — This article is about the mathematical discipline. For the informal notion in other parts of mathematics and science, see Mathematical model. In mathematics, model theory is the study of (classes of) mathematical structures (e.g. groups, fields,… …   Wikipedia

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• Formal group — In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were first defined in 1946 by S. Bochner. The term formal group sometimes means the same as formal group law,… …   Wikipedia