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

# Ring theory

• 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.