which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but...

) {\displaystyle R/(q_{i})} are indecomposable, so the primary decomposition is a decomposition into indecomposable modules, and thus every finitely generated...

them. Decomposition relies on chemical processes similar to digestion in animals; in fact, many sources use the words digestion and decomposition interchangeably...

generalizations. The primary decomposition formulation states that every finitely generated abelian group G is isomorphic to a direct sum of primary cyclic groups...

ideal of a Noetherian ring has a primary decomposition, that is, can be written as an intersection of finitely many primary ideals. This result is known as...

positive integer. Thus, a primary decomposition of (n) corresponds to representing (n) as the intersection of finitely many primary ideals. The Lasker–Noether...

decomposition. Decomposition can be a gradual process for organisms that have extended periods of dormancy. One can differentiate abiotic decomposition from biotic...

Look up decomposition, decompose, or perishable in Wiktionary, the free dictionary. Decomposition is the process through which organic matter is broken...

is not a prime power. Prime powers are also called primary numbers, as in the primary decomposition. Prime powers are powers of prime numbers. Every prime...

Lasker–Noether primary decomposition of ideals in commutative Noetherian rings. Specifically, if an ideal J is decomposed as a finite intersection of primary ideals...

p-group of prime power order Primary decomposition into primary ideals Primary ideals, concept in commutative algebra Primary number, positive integer power...

(algebra) Krull dimension Krull's principal ideal theorem Primary ideal Primary decomposition and the Lasker–Noether theorem Noether normalization lemma...

contributions to commutative algebra, which included proving the primary decomposition of the ideals of polynomial rings. His philosophical works and a...

m\times n} ⁠ matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an m × n {\displaystyle m\times n} complex...

ideal membership for polynomial rings. Hermann's algorithm for primary decomposition is still in contemporary use. From 1925 to 1927, Hermann worked...

The chemical decomposition of an explosive may take years, days, hours, or a fraction of a second. The slower processes of decomposition take place in...

Noetherian ring, each ideal has a primary decomposition, meaning that it can be written as an intersection of finitely many primary ideals (whose radicals are...

irredundant decomposition into tertiary ideals I = T 1 ∩ ⋯ ∩ T n {\displaystyle I=T_{1}\cap \dots \cap T_{n}} . Riley, J.A. (1962), "Axiomatic primary and tertiary...

matrix ring over a local serial ring. Such rings are also known as primary decomposable serial rings. References for each author can be found in Puninski...

the Lasker–Noether theorem, which extends Lasker's theorem on the primary decomposition of ideals of polynomial rings to all Noetherian rings. The Lasker–Noether...

handle decomposition is to a manifold what a CW-decomposition is to a topological space—in many regards the purpose of a handle decomposition is to have...

decomposable A module is called decomposable if it can be written as a direct sum of two non-zero submodules. decomposition group A decomposition group...

elementary concepts of commutative algebra including localization, primary decomposition, integral dependence, Noetherian and Artinian rings and modules...

microbial decomposition occurs. Temperature also affects soil moisture, which affects decomposition. Freeze-thaw cycles also affect decomposition—freezing...

R / I {\displaystyle R/I} ; this follows for instance from the primary decomposition of I. In a commutative Artinian ring, every maximal ideal is a minimal...

these calculations and improved them using the QCISD(T) method. The primary decomposition products were determined by this method to be SiCl2 and SiClH. Dichlorosilane...

Noetherian ring is a primary ideal, and consequently for Noetherian rings an irreducible decomposition is a primary decomposition. Every primary ideal of a principal...

the primary decomposition is a decomposition into indecomposable modules, so every finitely-generated module over a PID is completely decomposable. Explicitly...

used decomposition in the control field is to decompose a system into two or more lower-order subsystems, called lower-order subsystem decomposition here...

R-modules with R a principal ideal domain A and B are isomorphic as R-modules Primary decomposition (up to reordering) or invariant factor decomposition...