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algebraically closed group

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  • 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

  • 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

  • Group representation — In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group… …   Wikipedia

  • Absolute presentation of a group — In mathematics, one method of defining a group is by an absolute presentation.B. Neumann, The isomorphism problem for algebraically closed groups, in: Word Problems, Decision Problems, and the Burnside Problem in Group Theory, Amsterdam London… …   Wikipedia

  • Stable group — For stable groups in homotopy theory see stable homotopy group or direct limit of groups. In model theory, a stable group is a group that is stable in the sense of stability theory. An important class of examples is provided by groups of finite… …   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

  • Absolute Galois group — In mathematics, the absolute Galois group GK of a field K is the Galois group of K sep over K , where K sep is a separable closure of K . Alternatively it is the group of all automorphisms of the algebraic closure of K that fix K . The absolute… …   Wikipedia

  • 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

  • Brauer group — In mathematics, the Brauer group arose out of an attempt to classify division algebras over a given field K . It is an abelian group with elements isomorphism classes of division algebras over K , such that the center is exactly K . The group is… …   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

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