# abelian extension

- rozszerzenie abelowe

*English-Polish dictionary for engineers.
2013.*

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**Abelian extension**— In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is a cyclic group, we have a cyclic extension. More generally, a Galois extension is called solvable if its Galois group is… … Wikipedia**Abelian**— Abelian, in mathematics, is used in many different definitions, named after Norwegian mathematician Niels Henrik Abel:In group theory:*Abelian group, a group in which the binary operation is commutative **Category of abelian groups Ab has abelian … Wikipedia**Extension (mathematics)**— In mathematics, the word extension has many uses. See:Analysis* Carathéodory s extension theorem * Continuous linear extension * M. Riesz extension theorem * Krein extension theorem * Hahn Banach theoremAlgebra* Abelian extension * Algebraic… … Wikipedia**Abelian group**— For other uses, see Abelian (disambiguation). Abelian group is also an archaic name for the symplectic group Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product,… … Wikipedia**Abelian variety**— In mathematics, particularly in algebraic geometry, complex analysis and number theory, an Abelian variety is a projective algebraic variety that is at the same time an algebraic group, i.e., has a group law that can be defined by regular… … Wikipedia**Extension of scalars**— In abstract algebra, extension of scalars is a means of producing a module over a ring S from a module over another ring R, given a homomorphism f : R o S between them. Intuitively, the new module admits multiplication by more scalars than the… … Wikipedia**Timeline of abelian varieties**— This is a timeline of the theory of abelian varieties in algebraic geometry, including elliptic curves.Early history* c. 1000 Al Karaji writes on congruent numbers [ [http://www.cms.math.ca/Events/summer05/abs/pdf/hm.pdf PDF] ] eventeenth… … Wikipedia**Non-abelian class field theory**— In mathematics, non abelian class field theory is a catchphrase, meaning the extension of the results of class field theory, the relatively complete and classical set of results on abelian extensions of any number field K, to the general Galois… … Wikipedia**Group extension**— In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence:1 ightarrow N… … Wikipedia**Equations defining abelian varieties**— In mathematics, the concept of abelian variety is the higher dimensional generalization of the elliptic curve. The equations defining abelian varieties are a topic of study because every abelian variety is a projective variety. In dimension d ge; … Wikipedia**Semistable abelian variety**— In mathematics, a semistable abelian variety in Diophantine geometry is an abelian variety defined over a global or local field with reduction modulo all primes of restricted type.For an Abelian variety A defined over a field F with ring of… … Wikipedia