which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but...
26 KB (4,366 words) - 08:47, 7 November 2023
Structure theorem for finitely generated modules over a principal ideal domain (section Primary decomposition)
) {\displaystyle R/(q_{i})} are indecomposable, so the primary decomposition is a decomposition into indecomposable modules, and thus every finitely generated...
15 KB (2,160 words) - 18:51, 20 June 2024
Decomposers are organisms that break down dead or decaying organisms; they carry out decomposition, a process possible by only certain kingdoms, such as...
5 KB (556 words) - 22:37, 9 September 2024
generalizations. The primary decomposition formulation states that every finitely generated abelian group G is isomorphic to a direct sum of primary cyclic groups...
12 KB (1,658 words) - 07:13, 19 May 2024
Commutative algebra (section Primary decomposition)
positive integer. Thus, a primary decomposition of (n) corresponds to representing (n) as the intersection of finitely many primary ideals. The Lasker–Noether...
17 KB (2,020 words) - 15:41, 6 May 2024
(algebra) Krull dimension Krull's principal ideal theorem Primary ideal Primary decomposition and the Lasker–Noether theorem Noether normalization lemma...
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LU decomposition, a type of matrix factorization Permutation decomposition, decomposition of a permutation into disjoint cycles Primary decomposition, decomposition...
3 KB (370 words) - 00:14, 17 May 2024
p-group of prime power order Primary decomposition into primary ideals Primary ideals, concept in commutative algebra Primary number, positive integer power...
3 KB (376 words) - 20:53, 15 May 2024
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...
7 KB (1,084 words) - 11:47, 28 March 2024
science which studies decomposition is generally referred to as taphonomy from the Greek word taphos, meaning tomb. Decomposition can also be a gradual...
56 KB (6,406 words) - 08:41, 17 August 2024
Prime power (redirect from Primary number)
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...
4 KB (603 words) - 22:24, 31 August 2024
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...
86 KB (13,746 words) - 07:26, 5 September 2024
contributions to commutative algebra, which included proving the primary decomposition of the ideals of polynomial rings. His philosophical works and a...
112 KB (10,749 words) - 18:54, 2 September 2024
Dichlorosilane (section Decomposition)
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...
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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...
19 KB (1,873 words) - 02:49, 30 June 2024
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...
20 KB (2,773 words) - 10:09, 18 February 2024
Lasker–Noether primary decomposition of ideals in commutative Noetherian rings. Specifically, if an ideal J is decomposed as a finite intersection of primary ideals...
6 KB (979 words) - 18:00, 6 February 2024
Explosive (redirect from Primary explosives)
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...
72 KB (8,250 words) - 05:32, 9 September 2024
Serial module (redirect from Primary decomposable ring)
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...
16 KB (2,263 words) - 02:29, 26 June 2024
Ecosystem (section Decomposition)
microbial decomposition occurs. Temperature also affects soil moisture, which affects decomposition. Freeze-thaw cycles also affect decomposition—freezing...
64 KB (6,950 words) - 03:40, 28 August 2024
following: The primary decomposition of I : f ∞ {\displaystyle I:f^{\infty }} consists of the components of the primary decomposition of I that do not...
61 KB (9,883 words) - 03:42, 5 September 2024
Plant litter (redirect from Decomposing litter)
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...
30 KB (3,626 words) - 04:08, 3 December 2023
Gröbner basis computations do not allow one to compute directly the primary decomposition of I nor the prime ideals defining the irreducible components of...
61 KB (7,500 words) - 06:41, 31 July 2024
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...
66 KB (9,767 words) - 00:23, 7 July 2024
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...
127 KB (14,714 words) - 12:12, 9 September 2024
which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but...
65 KB (7,595 words) - 11:45, 9 September 2024
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...
12 KB (1,610 words) - 15:10, 12 February 2024
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...
6 KB (1,200 words) - 09:34, 5 May 2023
the primary decomposition is a decomposition into indecomposable modules, so every finitely-generated module over a PID is completely decomposable. Explicitly...
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pulmonarius and P. populinus. It is a saprotroph that acts as a primary decomposer of wood, especially deciduous trees, and beech trees in particular...
13 KB (1,396 words) - 09:18, 18 June 2024