primary decomposition

primary decomposition

[′prī‚mer·ē dē‚käm·pə′zish·ən]
(mathematics)
A primary decomposition of a submodule N of a module M is an expression of N as a finite intersection of primary submodules of M.
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Both the single and multiple rate nonisothermal methods were applied to determine the activation energy E and the preexponential factor A in the primary decomposition phases.
The selected lectures cover the topology and geometry of real singularities, singularities of mappings and the vanishing homology of images and discriminants, notes on non-isolated singularities, algorithms for primary decomposition in Singular, singularities of maps and characteristic classes, and centers and limit cycles in polynomial systems of ordinary differential equations.
So biochar was the major product along with vapors of primary decomposition of biomass.
The low biochar yield at higher temperature could either be due to the greater primary decomposition of the paper mulberry (Parihar 2007).
1, it may be established that C[O.sub.2] release from litter results from its primary decomposition and also from secondary decomposition of microbial biomass.
The results obtained on the failed sample included weight loss steps associated with the dehydrohalogenation of the polymer, the primary decomposition of the polymer, and the combustion of carbon black and char.
The primary decomposition products are tetrafluoroethylene (TFE) and difluorocarbondiradicals ([RCF.sub.2]).
However, B is an integrally closed Noetherian domain, and so we can replace factorization of functions by primary decomposition of principal ideals.
[intersection] [N.sub.r] a primary decomposition of N in M with associated prime ideals [Mathematical Expression Omitted].
f) Let I [subset] N [(omega)] be an ideal with compact zero-set, and let I = [I.sub.1][subset]...[subset][I.sub.r] be a primary decomposition with associated prime ideals [p.sub.i] = [Mathematical Expressions Omitted], 1 [less than or equal to] i [less than or equal to] r.
Section 4 is devoted to separation; in fact, we prove more, namely, that primary decompositions of modules are preserved by the base change [Mathematical Expression Omitted].
Let us remark that the latter proof hides primary decompositions. In fact, we have actually shown that primary decompositions of principal ideals are preserved by the base change [Mathematical Expression Omitted].