In algebra, a commutative Noetherian ring A is said to have the approximation property with respect to an ideal I if each finite system of polynomial...

concerning polynomial approximations of complex functions. Stone, M. H. (1937), "Applications of the Theory of Boolean Rings to General Topology", Transactions...

study of ring properties that are not specific to commutative rings. This distinction results from the high number of fundamental properties of commutative...

number theory, commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique factorization domains, regular rings, group...

homotopy theory on them, which is called the simplicial homotopy theory. Highly structured ring spectrum Homotopy type theory Pursuing Stacks Shape theory Moduli...

resulting ring called an operational Chow ring. On technical levels, a bivariant theory is a mix of a homology theory and a cohomology theory. In general...

of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such...

or through set theory. In logic, equality is a primitive predicate (a statement that may have free variables) with the reflexive property (called the law...

combinations of atomic orbitals (LCAO). These approximations are made by applying the density functional theory (DFT) or Hartree–Fock (HF) models to the Schrödinger...

basis by Artin's approximation theorem. A formal universal deformation is by definition a formal scheme over a complete local ring, with special fiber...

polynomials for many other properties. In 1952, Cornelius Lanczos showed that the Chebyshev polynomials are important in approximation theory for the solution of...

In algebraic group theory, approximation theorems are an extension of the Chinese remainder theorem to algebraic groups G over global fields k. Eichler...

dyadic rational numbers form a ring, lying between the ring of integers and the field of rational numbers. This ring may be denoted Z [ 1 2 ] {\displaystyle...

integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational...

{\displaystyle V} ⁠. For example, the theory of Gröbner bases was introduced by Bruno Buchberger for ideals in a polynomial ring R = K[x1, ..., xn] over a field...

geometric properties of figures derived from them, such as in the formula for the volume of a dodecahedron. Hurwitz's theorem in Diophantine approximations states...

particularly in functional analysis and ring theory, an approximate identity is a net in a Banach algebra or ring (generally without an identity) that acts...

Mathematics: Approximation theory — Arakelov theory — Asymptotic theory — Bifurcation theory — Catastrophe theory — Category theory — Chaos theory — Choquet...

elementary problem in ring theory is how to turn a rng (which is like a ring that might not have a multiplicative identity) into a ring. The most efficient...

Simplicial complex Polytope Triangulation Barycentric subdivision Simplicial approximation theorem Abstract simplicial complex Simplicial set Simplicial category...

cover other objects as an approximation, and (dually) cogenerators are objects which envelope other objects as an approximation. More precisely: A generator...

the exactness property of completion. The lemma also plays a key role in the study of ℓ-adic sheaves. Let I be an ideal in a Noetherian ring R; let M be...

four approximations: A limiting law for additivity rules. Zero-order approximation. Additivity of atomic properties. First-order approximation. Additivity...

(Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is that it deals...

Design theory is a study of combinatorial designs, which are collections of subsets with certain intersection properties. Partition theory studies various...

considered difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. But in 1916, the astrophysicist Karl Schwarzschild...

abstract mathematics called category theory, a projective cover of an object X is in a sense the best approximation of X by a projective object P. Projective...

mathematics, the adele ring of a global field (also adelic ring, ring of adeles or ring of adèles) is a central object of class field theory, a branch of algebraic...

In commutative algebra, a Krull ring, or Krull domain, is a commutative ring with a well behaved theory of prime factorization. They were introduced by...

case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration. Mathematics is essential...