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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...

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

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

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

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

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

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

In mathematics, the Artin approximation theorem is a fundamental result of Michael Artin (1969) in deformation theory which implies that formal power...

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

polynomial ring R = K[x1, ..., xn] over a field. The construction of the unital zero algebra over a free R-module allows extending this theory as a Gröbner...

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

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

structure and properties of matter. All bonds can be described by quantum theory, but, in practice, simplified rules and other theories allow chemists...

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...

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...

number theory). One may also study real numbers in relation to rational numbers, for example, as approximated by the latter (Diophantine approximation). The...

Functions of a complex variable (including approximation theory in the complex domain) 31: Potential theory 32: Several complex variables and analytic...

(1970), Commutative algebra Matsumura, Hideyuki (1986). Commutative ring theory. Cambridge Studies in Advanced Mathematics. Vol. 8. Cambridge University...

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...

atom, compared to the valence shell model. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much...