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Why $R/AB$ is cyclic?

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#abstract-algebra #modules #ideals
1.1k
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The difference between the ring version and module version of Chinese Remainder Thereom.

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#abstract-algebra #ring-theory #modules #ideals #chinese-remainder-theorem
330
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What are some examples of principal, proper ideals that have height at least $2$?

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#ring-theory #commutative-algebra #ideals #big-list
640
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Factorising ideals in the ring of integers of a quadratic field

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#algebraic-number-theory #ideals
190
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How to prove that an ideal can not be generated by 2 elements

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#abstract-algebra #algebraic-geometry #ring-theory #commutative-algebra #ideals
193
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Factoring the Ring of Integers into Ideals

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#ring-theory #ideals #maximal-and-prime-ideals
539
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Uniqueness of prime ideals of $\mathbb F_p[x]/(x^2)$

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#ring-theory #algebraic-number-theory #ideals #maximal-and-prime-ideals
665
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Quotient of the ring of integers of a quadratic field by the ideal generated by a split integer prime.

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#abstract-algebra #ring-theory #algebraic-number-theory #ideals
1.8k
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Closed points are dense in $\operatorname{Spec} A$

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#algebraic-geometry #proof-verification #ideals #maximal-and-prime-ideals
614
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Maximal ideals of finite algebra over a local ring

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#commutative-algebra #ideals #maximal-and-prime-ideals
820
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Simple modules over R isomorphic to R/I

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#linear-algebra #field-theory #modules #ideals
2.3k
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Example of ideal generated by two elements

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#abstract-algebra #ring-theory #ideals
366
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The annihilator induces a module

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#linear-algebra #ring-theory #modules #ideals
1.5k
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On the minimal set of generators of monomial ideals in $\mathbb{C}[x,y]$.

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#abstract-algebra #commutative-algebra #ideals
111
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Show if $2$ and $1+\sqrt{-5}$ belong to the same principal ideal $I$ of $\mathbb{Z}[\sqrt{-5}]$ then $I=\mathbb{Z}[\sqrt{-5}]$.

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#abstract-algebra #ideals

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