automorphism ring

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• Automorphism — In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms… …   Wikipedia

• Inner automorphism — In abstract algebra an inner automorphism is a function which, informally, involves a certain operation being applied, then another one (x) performed, and then the initial operation being reversed. Sometimes this has a net effect ( take off shoes …   Wikipedia

• Class automorphism — In mathematics, in the realm of group theory, a class automorphism is an automorphism of a group that sends each element to within its conjugacy class. The class automorphisms form a subgroup of the automorphism group. Some facts: Every inner… …   Wikipedia

• Inversive ring geometry — In mathematics, inversive ring geometry is the extension to the context of associative rings, of the concepts of projective line, homogeneous coordinates, projective transformations, and cross ratio, concepts usually built upon rings that happen… …   Wikipedia

• Finite field — In abstract algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains only finitely many elements. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, and… …   Wikipedia

• General linear group — Group theory Group theory …   Wikipedia

• Leech lattice — In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24 dimensional Euclidean space E24 found by John Leech (1967). Contents 1 History 2 Characterization 3 Properties …   Wikipedia

• Splitting of prime ideals in Galois extensions — In mathematics, the interplay between the Galois group G of a Galois extension L of a number field K, and the way the prime ideals P of the ring of integers OK factorise as products of prime ideals of OL, provides one of the richest parts of… …   Wikipedia

• List of group theory topics — Contents 1 Structures and operations 2 Basic properties of groups 2.1 Group homomorphisms 3 Basic types of groups …   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

• Frobenius endomorphism — In commutative algebra and field theory, which are branches of mathematics, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of rings with prime characteristic p , a class importantly including fields. The… …   Wikipedia