algebraically closed


algebraically closed
алгебраически замкнутый

English-Russian dictionary of technical terms. 2014.

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  • algebraically closed — adjective Containing all roots of single variable polynomials in its elements. According to the fundamental theorem of algebra, the field of complex numbers is algebraically closed …   Wiktionary

  • Algebraically 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,… …   Wikipedia

  • Algebraically closed group — In mathematics, in the realm of group theory, a group A is algebraically closed if any finite set of equations and inequations that make sense in A already have a solution in A . This idea will be made precise later in the article.Informal… …   Wikipedia

  • algebraically closed field — Math. a field in which every polynomial equation with coefficients that are elements of the field has at least one root in the field, as the field of complex numbers. * * * …   Universalium

  • algebraically closed field — Math. a field in which every polynomial equation with coefficients that are elements of the field has at least one root in the field, as the field of complex numbers …   Useful english dictionary

  • Quasi-algebraically closed field — In mathematics, a field F is called quasi algebraically closed (or C1) if for every non constant homogeneous polynomial P over F has a non trivial zero provided the number of its variables is more than its degree. In other words, if P is a non… …   Wikipedia

  • Pseudo algebraically closed field — In mathematics, a field K is pseudo algebraically closed (usually abbreviated by PAC) if one of the following equivalent conditions holds:*Each absolutely irreducible variety V defined over K has a K rational point. *Each absolutely irreducible… …   Wikipedia

  • Closed-form expression — Closed formula redirects here. For closed formula in the sense of a logic formula with no free variables, see Sentence (mathematical logic). In mathematics, an expression is said to be a closed form expression if it can be expressed analytically… …   Wikipedia

  • Differentially closed field — In mathematics, a differential field K is differentially closed if every finite system of differential equations with a solution in some differential field extending K already has a solution in K. This concept was introduced by Robinson (1959).… …   Wikipedia

  • Real closed field — In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… …   Wikipedia

  • Existentially closed model — In model theory, a branch of mathematical logic, the notion of an existentially closed model of a theory generalizes the notions of algebraically closed fields (for the theory of fields), real closed fields (for the theory of ordered fields),… …   Wikipedia