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]: Add brief definition or description
• Local ring [r]: Add brief definition or description
• Localisation (ring theory) [r]: Add brief definition or description
• Manin obstruction [r]: Add brief definition or description
• Monoid [r]: Add brief definition or description
• Noetherian module [r]: Add brief definition or description
• Noetherian ring [r]: Add brief definition or description
• Normaliser [r]: Add brief definition or description
• Polynomial ring [r]: Add brief definition or description
• Resolution (algebra) [r]: Add brief definition or description
• Resultant (algebra) [r]: Add brief definition or description
• S-unit [r]: Add brief definition or description
• Splitting field [r]: Add brief definition or description
• Stably free module [r]: Add brief definition or description
• Symmetric group [r]: Add brief definition or description
• Szpiro's conjecture [r]: Add brief definition or description
• Weierstrass preparation theorem [r]: Add brief definition or description