the Cohen structure theorem, introduced by Cohen (1946), describes the structure of complete Noetherian local rings. Some consequences of Cohen's structure...

the Cohen structure theorem for complete Noetherian local rings. In 1946 he proved the unmixedness theorem for power series rings. As a result, Cohen–Macaulay...

economic theory; it forms the basis for modern thinking on capital structure. The basic theorem states that in the absence of taxes, bankruptcy costs, agency...

unmixedness theorem for polynomial rings, and for Irvin Cohen (1946), who proved the unmixedness theorem for formal power series rings. All Cohen–Macaulay...

by p. Cohen rings are used in the Cohen structure theorem for complete Noetherian local rings. Norm field Cohen, I. S. (1946), "On the structure and ideal...

conjectures List of data structures List of derivatives and integrals in alternative calculi List of equations List of fundamental theorems List of hypotheses...

configuration – this result was incorrectly attributed and is known as the Cohen-Kong theorem. In 2000, Gajardo et al. showed a construction that calculates any...

include Wilfried Brauer, Karl-Otto Stöhr and Jürgen Neukirch. Cohen structure theorem Jacobson ring Local ring Prime ideal Real algebraic geometry Regular...

local ring. Complete Noetherian local rings are classified by the Cohen structure theorem. In algebraic geometry, especially when R is the local ring of...

lemma) A complete ring has much simpler structure than a commutative ring. This owns to the Cohen structure theorem, which says, roughly, that a complete...

{\displaystyle {\widehat {R/I}}\cong {\widehat {R}}/{\widehat {I}}.} Cohen structure theorem (equicharacteristic case). Let R be a complete local Noetherian...

In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved in the early 1960s...

Hungerford's theorem employs Cohen's structure theorems for complete local rings. Arguing as in Example 3. above and using the Zariski-Samuel theorem, it is...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

inferential steps and often use various rules of inference to establish the theorem they intend to demonstrate. Rules of inference are definitory rules—rules...

In homological algebra, a branch of mathematics, a matrix factorization is a tool used to study infinitely long resolutions, generally over commutative...

theory, the Kurosh subgroup theorem describes the algebraic structure of subgroups of free products of groups. The theorem was obtained by Alexander Kurosh...

extended this structure theorem to case of codimension 4. Eisenbud (1995), pg 525. Eisenbud (1995), Proposition 21.5. Huneke (1999), Theorem 9.1. Lam (1999)...

Löwenheim–Skolem theorem, which says that first-order logic cannot control the cardinalities of infinite structures. Skolem realized that this theorem would apply...

In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample...

injective resolution, then R {\displaystyle R} is a Cohen–Macaulay ring. The Intersection Theorem. If M ⊗ R N ≠ 0 {\displaystyle M\otimes _{R}N\neq 0}...

compact module Reflexive module Concepts and theorems Composition series Length of a module Structure theorem for finitely generated modules over a principal...

density theorem determines the structure of primitive rings Goldie's theorem determines the structure of semiprime Goldie rings The Zariski–Samuel theorem determines...

mathematics, Stickelberger's theorem is a result of algebraic number theory, which gives some information about the Galois module structure of class groups of cyclotomic...

divisor Chinese remainder theorem Field (mathematics) Algebraic number field Polynomial ring Integral domain Boolean algebra (structure) Principal ideal domain...

sentences satisfied by a structure is also called the theory of that structure. It's a consequence of Gödel's completeness theorem (not to be confused with...

The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and...

inequality, we can assume A {\displaystyle A} is complete. Then by Cohen's structure theorem, we can write A = A 1 / a 1 A 1 {\displaystyle A=A_{1}/a_{1}A_{1}}...

local analysis was started by the Sylow theorems, which contain significant information about the structure of a finite group G for each prime number...

son of Sigismund Steinitz, a Jewish coal merchant, and his wife Auguste Cohen; he had two brothers. He studied at the University of Breslau and the University...