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...

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

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

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

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

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...

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

(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...

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...

1419. Cochran, Tim D.; Harvey, Shelly; Leidy, Constance (2011). "Primary decomposition and the fractal nature of knot concordance". Mathematische Annalen...

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...

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

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

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...

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

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

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

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...

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...

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...

K\subseteq (I:J)} . The ideal quotient is useful for calculating primary decompositions. It also arises in the description of the set difference in algebraic...

greater than other soil arthropods, therefore, they are significant primary decomposers of leaf litter in their habitat. "Australian Faunal Directory: Arcitalitrus...

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

In computer algebra, a triangular decomposition of a polynomial system S is a set of simpler polynomial systems S1, ..., Se such that a point is a solution...

following: The primary decomposition of I : f ∞ {\displaystyle I:f^{\infty }} consists of the components of the primary decomposition of I that do not...

Gröbner basis computations do not allow one to compute directly the primary decomposition of I nor the prime ideals defining the irreducible components of...