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Finitely generated abelian group
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ideal domain, which in turn admits further generalizations. The primary decomposition formulation states that every finitely generated abelian group GIndecomposable module (705 words) [view diff] exact match in snippet view article find links to article
for finitely generated modules over a principal ideal domain: the primary decomposition is a decomposition into indecomposable modules, so every finitely-generatedSilver hyponitrite (639 words) [view diff] exact match in snippet view article find links to article
light. The anhydrous compound decomposes in vacuum at 158 °C. The primary decomposition products are silver(I) oxide Ag 2O and nitrous oxide N 2O. HoweverDichlorosilane (600 words) [view diff] exact match in snippet view article find links to article
these calculations and improved them using the QCISD(T) method. The primary decomposition products were determined by this method to be SiCl2 and SiClH. DichlorosilaneShelly Harvey (268 words) [view diff] exact match in snippet view article find links to article
S2CID 8072597. Cochran, Tim D.; Harvey, Shelly; Leidy, Constance (2011), "Primary decomposition and the fractal nature of knot concordance", Mathematische AnnalenCanonical form (1,873 words) [view diff] exact match in snippet view article find links to article
R-modules with R a principal ideal domain A and B are isomorphic as R-modules Primary decomposition (up to reordering) or invariant factor decompositionNitrile anion (999 words) [view diff] exact match in snippet view article find links to article
G. J. W.; Hajek, M. K.; Awang, D. V. C. (1970). "Isolation of primary decomposition products of azides. II. Azidopyrazoles". J. Org. Chem. 35 (7): 2215Ideal theory (1,095 words) [view diff] exact match in snippet view article find links to article
Another is the integral closure of an ideal. Given an irredundant primary decomposition I = ∩ Q i {\displaystyle I=\cap Q_{i}} , the intersection of Q iMacsyma (2,533 words) [view diff] exact match in snippet view article find links to article
Patrizia; Trager, Barry; Zacharias, Gail (1988). "Gröbner bases and primary decomposition of polynomial ideals". Journal of Symbolic Computation. 6 (2–3):Dense submodule (1,016 words) [view diff] exact match in snippet view article find links to article
ISBN 978-0-387-98428-5, MR 1653294 Storrer, Hans H. (1972), "On Goldman's primary decomposition", Lectures on Rings and Modules (Tulane Univ. Ring and OperatorPrincipal ideal ring (1,281 words) [view diff] exact match in snippet view article find links to article
ring. The proof applies the Chinese Remainder theorem to a minimal primary decomposition of the zero ideal. There is also the following result, due to Hungerford:Triangular decomposition (1,610 words) [view diff] exact match in snippet view article find links to article
York, Dover Publications A. M. Steel Conquering inseparability: Primary decomposition and multivariate factorization over algebraic function fields ofSpectrum of a ring (3,908 words) [view diff] exact match in snippet view article find links to article
to the (reduced) points of the variety, with multiplicity; the primary decomposition of the module corresponds to the unreduced points of the variety;Tim Cochran (680 words) [view diff] exact match in snippet view article find links to article
1419. Cochran, Tim D.; Harvey, Shelly; Leidy, Constance (2011). "Primary decomposition and the fractal nature of knot concordance". Mathematische AnnalenNitrapyrin (780 words) [view diff] exact match in snippet view article find links to article
plants. The compound itself tends not to persist in nature. The primary decomposition is the hydrolysis of the trichloromethyl functional group, resultingAlgebraic geometry (7,405 words) [view diff] exact match in snippet view article find links to article
Gröbner basis computations do not allow one to compute directly the primary decomposition of I nor the prime ideals defining the irreducible components ofÉléments de mathématique (3,074 words) [view diff] case mismatch in snippet view article find links to article
associés et décomposition primaire 4 Associated Prime Ideals and Primary Decomposition Algèbre commutative: Chapitres 5 à 7 5 Entiers 5 Integers 6 ValuationsCraig Huneke (520 words) [view diff] exact match in snippet view article find links to article
pg. 53-89 With David Eisenbud, W. Vasconcelos Direct methods for primary decomposition, Inventiones Mathematicae, volume 110, 1992, pg. 207-236 UniformEmmy Noether (14,689 words) [view diff] exact match in snippet view article find links to article
the Lasker–Noether theorem, which extends Lasker's theorem on the primary decomposition of ideals of polynomial rings to all Noetherian rings. The Lasker–NoetherList of inventions and discoveries by women (7,595 words) [view diff] exact match in snippet view article find links to article
means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not