# Serge Lang/Related Articles

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*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.
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