Serge Lang > Related Articles
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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]
