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Show that $(X_{k_1}^{a_1},...,X_{k_s}^{a_s})$ is $(X_{k_1},...,X_{k_s})$-primary

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#abstract-algebra #monomial-ideals #ideals
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Easy explanation on primary decomposition of ideals.

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#commutative-algebra #ideals #monomial-ideals
165
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Leading term ideal irreducible iff the ideal is irreducible?

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#commutative-algebra #irreducible-polynomials #monomial-ideals
119
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Decomposition of a monomial ideal

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#commutative-algebra #ideals #monomial-ideals
64
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A concrete example of an ideal $I\subseteq K[x_1,\ldots,x_n]$ and coprime polynomials $f,g$ such that $(I,f)\cap (I,g)\neq (I,fg)$

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#polynomials #commutative-algebra #monomial-ideals
660
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Primary decomposition of ideals

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#commutative-algebra #ideals #monomial-ideals
603
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Associated primes of powers of a monomial ideal

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#commutative-algebra #monomial-ideals
890
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Prove that ideal generated by.... Is a monomial ideal

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#abstract-algebra #polynomials #commutative-algebra #ideals #monomial-ideals
374
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Rees algebra of a monomial ideal

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#commutative-algebra #monomial-ideals
246
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Depth of ideals in a commutative ring

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#commutative-algebra #monomial-ideals
3.3k
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Primary decomposition of a monomial ideal

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#commutative-algebra #ideals #monomial-ideals
732
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Primary decomposition of an ideal

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#commutative-algebra #monomial-ideals
377
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Reference to this rule $I = (ab) + J$, then $I = ((a) + J) \cap ((b) + J)$

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#abstract-algebra #commutative-algebra #monomial-ideals
438
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P-primary Monomial Ideal

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#abstract-algebra #commutative-algebra #ideals #monomial-ideals
172
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Graded Betti Numbers of a Stable Monomial Ideal

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#ring-theory #commutative-algebra #ideals #monomial-ideals #betti-numbers

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