Serge Lang/Related Articles

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A list of Citizendium articles, and planned articles, about Serge Lang.
See also changes related to Serge Lang, or pages that link to Serge Lang or to this page or whose text contains "Serge Lang".

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  • Abelian variety [r]: A complete non-singular projective variety which is also an algebraic group, necessarily abelian; a complex torus. [e]
  • Algebra over a field [r]: A ring containing an isomorphic copy of a given field in its centre. [e]
  • Algebraic independence [r]: The property of elements of an extension field which satisfy only the trivial polynomial relation. [e]
  • Algebraic number field [r]: A field extension of the rational numbers of finite degree; a principal object of study in algebraic number theory. [e]
  • Algebraic number [r]: A complex number that is a root of a polynomial with rational coefficients. [e]
  • Centraliser [r]: The set of all group elements which commute with every element of a given subset. [e]
  • Centre of a ring [r]: The subring of a ring consisting of all elements which commute with every element of the ring. [e]
  • Complement (linear algebra) [r]: A pair of subspaces which form an (internal) direct sum. [e]
  • Conductor of an abelian variety [r]: A measure of the nature of the bad reduction at some prime. [e]
  • Conjugation (group theory) [r]: The elements of any group that may be partitioned into conjugacy classes. [e]
  • Content (algebra) [r]: The highest common factor of the coefficients of a polynomial. [e]
  • Cyclotomic field [r]: An algebraic number field generated over the rational numbers by roots of unity. [e]
  • Derivation (mathematics) [r]: A map defined on a ring which behaves formally like differentiation: D(x.y)=D(x).y+x.D(y). [e]
  • Discriminant of a polynomial [r]: An invariant of a polynomial which vanishes if it has a repeated root: the product of the differences between the roots. [e]
  • Division ring [r]: (or skew field), In algebra it is a ring in which every non-zero element is invertible. [e]
  • Exact sequence [r]: A sequence of algebraic objects and morphisms which is used to describe or analyse algebraic structure. [e]
  • Field automorphism [r]: An invertible function from a field onto itself which respects the field operations of addition and multiplication. [e]
  • Field theory (mathematics) [r]: A subdiscipline of abstract algebra that studies fields, which are mathematical constructs that generalize on the familiar concepts of real number arithmetic. [e]
  • Galois theory [r]: Algebra concerned with the relation between solutions of a polynomial equation and the fields containing those solutions. [e]
  • Group (mathematics) [r]: Set with a binary associative operation such that the operation admits an identity element and each element of the set has an inverse element for the operation. [e]
  • Group theory [r]: Branch of mathematics concerned with groups and the description of their properties. [e]
  • Idempotence [r]: The property of an operation that repeated application has no effect. [e]
  • Inner product [r]: A bilinear or sesquilinear form on a vector space generalising the dot product in Euclidean spaces. [e]
  • Integral domain [r]: A commutative ring in which the product of two non-zero elements is again non-zero. [e]
  • Linear independence [r]: The property of a system of elements of a module or vector space, that no non-trivial linear combination is zero. [e]
  • Local ring [r]: A ring with a unique maximal ideal. [e]
  • Localisation (ring theory) [r]: An extension ring in which elements of the base ring become invertible. [e]
  • Manin obstruction [r]: A measure of the failure of the Hasse principle for geometric objects. [e]
  • Monoid [r]: An algebraic structure with an associative binary operation and an identity element. [e]
  • Noetherian module [r]: Module in which every ascending sequence of submodules has only a finite number of distinct members. [e]
  • Noetherian ring [r]: A ring satisfying the ascending chain condition on ideals; equivalently a ring in which every ideal is finitely generated. [e]
  • Normaliser [r]: The elements of a group which map a given subgroup to itself by conjugation. [e]
  • Polynomial ring [r]: Ring formed from the set of polynomials in one or more variables with coefficients in another ring. [e]
  • Resolution (algebra) [r]: An exact sequence which is used to describe the structure of a module. [e]
  • Resultant (algebra) [r]: An invariant which determines whether or not two polynomials have a factor in common. [e]
  • S-unit [r]: An element of an algebraic number field which has a denominator confined to primes in some fixed set. [e]
  • Splitting field [r]: A field extension generated by the roots of a polynomial. [e]
  • Stably free module [r]: A module which is close to being free: the direct sum with some free module is free. [e]
  • Symmetric group [r]: The group of all permutations of a set, that is, of all invertible maps from a set to itself. [e]
  • Szpiro's conjecture [r]: A relationship between the conductor and the discriminant of an elliptic curve. [e]
  • Weierstrass preparation theorem [r]: A description of a canonical form for formal power series over a complete local ring. [e]