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...

Decomposers are organisms that break down dead or decaying organisms; they carry out decomposition, a process possible by only certain kingdoms, such as...

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...

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

LU decomposition, a type of matrix factorization Permutation decomposition, decomposition of a permutation into disjoint cycles Primary decomposition, decomposition...

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

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...

science which studies decomposition is generally referred to as taphonomy from the Greek word taphos, meaning tomb. Decomposition can also be a gradual...

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...

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...

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

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...

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...

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...

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...

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...

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

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

there is a thin litter layer due to the rapid decomposition, while in boreal forests, the rate of decomposition is slower and leads to the accumulation of...

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

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...

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...

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

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...

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...

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

 pulmonarius and P. populinus. It is a saprotroph that acts as a primary decomposer of wood, especially deciduous trees, and beech trees in particular...