Ring theory

2017-07-27T19:35:19+03:00[Europe/Moscow] en true Frobenius endomorphism, Integer, Integral domain, Ring (mathematics), Semisimple module, Commutative ring, Integral element, Regular local ring, Unit (ring theory), Symmetric algebra, Torsion-free module, Geometric algebra, Classification of Clifford algebras, Quadratic integer, Jacobson ring flashcards Ring theory
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  • Frobenius endomorphism
    In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic p, an important class which includes finite fields.
  • Integer
    An integer (from the Latin integer meaning "whole") is a number that can be written without a fractional component.
  • Integral domain
    In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.
  • Ring (mathematics)
    In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
  • Semisimple module
    In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts.
  • Commutative ring
    In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
  • Integral element
    In commutative algebra, an element b of a commutative ring B is said to be integral over A, a subring of B, if there are n ≥ 1 and such that That is to say, b is a root of a monic polynomial over A.
  • Regular local ring
    In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension.
  • Unit (ring theory)
    In mathematics, an invertible element or a unit in a (unital) ring R is any element u that has an inverse element in the multiplicative monoid of R, i.
  • Symmetric algebra
    In mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field K is the free commutative unital associative algebra over K containing V.
  • Torsion-free module
    In algebra, a torsion-free module is a module over a ring such that 0 is the only element annihilated by a regular element (non zero-divisor) of the ring.
  • Geometric algebra
    A geometric algebra (GA) is a Clifford algebra of a vector space over the field of real numbers endowed with a quadratic form.
  • Classification of Clifford algebras
    In abstract algebra, in particular in the theory of nondegenerate quadratic forms on vector spaces, the structures of finite-dimensional real and complex Clifford algebras have been completely classified.
  • Quadratic integer
    In number theory, quadratic integers are a generalization of the integers to quadratic fields.
  • Jacobson ring
    In algebra, a Hilbert ring or a Jacobson ring is a ring such that every prime ideal is an intersection of primitive ideals.