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$N(R)$ when $R$ is a P.I. ring

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#abstract-algebra #ring-theory #ideals #noncommutative-algebra
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Show that the union of a chain of ideals is an ideal.

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#abstract-algebra #ideals
271
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Ideal quotient is principal

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#abstract-algebra #ideals
270
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Sum of nil right ideals as an ideal

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#abstract-algebra #ring-theory #ideals #noncommutative-algebra
862
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The ideals $\langle y-x-1\rangle$ and $\langle x-2,y-3\rangle$ in $\mathbb C[x,y]$ are prime

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
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Definition of primary ideal

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#commutative-algebra #ideals
58
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Can we find ( characterize ) all non-zero commutative Artinian rings $R$ for which $-1 , 1$ are the only units of $R$ ?

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#ring-theory #ideals #artinian
74
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Let $A$ a Noetherian ring and $ q \in\mathrm{Spec} (A)$. Then $q^{(n)} A_q=q^{n}A_q$.

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#proof-verification #commutative-algebra #ideals
49
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Is a ring R, modulo an ideal I (generated by x), then modulo an ideal J (generated by n) the same as R modulo the ideal generated by (n,x)?

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#abstract-algebra #ideals
303
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Problems with proof of Krull's height theorem

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#ring-theory #ideals
667
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Finding the maximal ideals of the quotient of a polynomial ring by an ideal

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#abstract-algebra #algebraic-geometry #ring-theory #commutative-algebra #ideals
79
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Direct Summands of PI Rings as Right Ideals

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#abstract-algebra #ring-theory #ideals #noncommutative-algebra
288
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About the discriminant ideal

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#commutative-algebra #ideals #dedekind-domain #discriminant
202
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Let $R$ be a finite commutative ring such that distinct ideals of $R$ have distinct orders (size). Is $R$ a PIR?

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#abstract-algebra #ring-theory #ideals #finite-rings
78
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Equivalences for a Banach lattice

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#banach-spaces #ideals #normed-spaces #vector-lattices #banach-lattices

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