algebraic extension
51Gonality 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… …
52HNN extension — In mathematics, the HNN extension is a basic construction of combinatorial group theory.Introduced in a 1949 paper Embedding Theorems for Groups [ cite journal|title=Embedding Theorems for Groups|journal=Jornal of the London Mathematical… …
53Homotopy extension property — In mathematics, in the area of algebraic topology, the homotopy extension property indicates when a homotopy can be extended to another one, so that the original homotopy is simply the restriction of the extended homotopy.DefinitionGiven A subset …
54Essential extension — In mathematics, specifically module theory, given a ring R and R modules :Msubseteq E, the module E is an essential extension if for every nonzero submodule :Nsubseteq E, we have:Ncap M e 0. Also, M is then said to be an essential submodule of E …
55Field (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 …
56Glossary 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… …
57Algebraically closed field — In mathematics, a field F is said to be algebraically closed if every polynomial in one variable of degree at least 1, with coefficients in F , has a root in F . ExamplesAs an example, the field of real numbers is not algebraically closed,… …
58Field of definition — In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong. Given polynomials, with coefficients in a field K , it may not be obvious… …
59Fundamental theorem of algebra — In mathematics, the fundamental theorem of algebra states that every non constant single variable polynomial with complex coefficients has at least one complex root. Equivalently, the field of complex numbers is algebraically closed.Sometimes,… …
60Dedekind domain — In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily …
