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A confustion about the proof of Primary Decomposition theorem

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#linear-algebra #linear-transformations #primary-decomposition
278
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How to find the cyclic vectors when finding the Rational form of a given matrix?

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#linear-algebra #matrices #linear-transformations #cyclic-decomposition #primary-decomposition
190
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Decomposition in irreducible factors in a factor ring

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#commutative-algebra #prime-numbers #prime-factorization #primary-decomposition
76
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Find inner product that meets primary decomposition criterias

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#linear-algebra #inner-products #direct-sum #primary-decomposition
126
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If $W$ is T-invariant, $W=(W\cap W_{1})\oplus\cdots\oplus (W\cap W_{k})$

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#linear-algebra #invariant-theory #primary-decomposition
142
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On cancelling $\mathfrak m$-primary ideal of regular local ring $(R,\mathfrak m)$

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#commutative-algebra #modules #krull-dimension #regular-rings #primary-decomposition
109
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Artin-Rees property in commutative Noetherian rings with unit

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#ring-theory #commutative-algebra #noetherian #primary-decomposition
448
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Length of a module is sum of length of modules localization at each associated prime.

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#abstract-algebra #commutative-algebra #modules #primary-decomposition
86
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Embedded primes in a finitely generated algebra over an algebraically closed field

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#algebraic-geometry #polynomials #commutative-algebra #field-theory #primary-decomposition
232
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Writing a projective scheme as a union of irreducible subschemes.

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#algebraic-geometry #primary-decomposition
411
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Primary ideals are those whose quotient has irreducible prime spectrum.

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#abstract-algebra #commutative-algebra #ideals #primary-decomposition
58
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Factorization in the three variable function

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#calculus #multivariable-calculus #stochastic-processes #factoring #primary-decomposition
58
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Intersection of ideals and primary ideals

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#ring-theory #maximal-and-prime-ideals #primary-decomposition
544
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The notion of $P$-primary component

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#abstract-algebra #commutative-algebra #maximal-and-prime-ideals #primary-decomposition
56
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If $B$ is an $A$-algebra of Noetherian rings then $\text{Ass}_{A}M=\{f^{-1}(p):p \in \text{Ass}_{B}M\}$ for a f.g. $B$-module $M.$

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#abstract-algebra #ring-theory #commutative-algebra #modules #primary-decomposition

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