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Every element in a ring different from 0 is invertible

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#abstract-algebra #ring-theory
4.7k
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$M$ is a simple module if and only if $M \cong R/I$ for some $I$ maximal ideal in $R$.

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#abstract-algebra #ring-theory #modules
156
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If $k[X]/f = k[X]/g$, does $f = g$?

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#polynomials #ring-theory #field-theory
101
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Constructing noncommutative nilpotent rings of given index

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#ring-theory #examples-counterexamples #big-list #noncommutative-algebra
251
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Prove there exists a unique polynomial

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#abstract-algebra #elementary-number-theory #ring-theory
3.4k
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What is an $R$-algebra?

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#abstract-algebra #ring-theory #modules #definition #algebras
2k
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Vector space as simple $K[x]$-module

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#abstract-algebra #ring-theory #vector-spaces #modules
2.8k
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Why are there so many universal properties in math?

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#abstract-algebra #ring-theory #category-theory #field-theory
391
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Unique maximal ideal in the ring of fraction

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#ring-theory #ideals
5.1k
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What is a clever proof of Hilbert's basis theorem?

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#abstract-algebra #ring-theory #commutative-algebra #noetherian
416
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Justify: $R$ is commutative

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#ring-theory
342
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Zerodivisors in polynomial rings over a non-commutative ring

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#abstract-algebra #ring-theory #noncommutative-algebra
410
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Suppose that $K$ is a field and that $f$ and $g$ are relatively prime in $K[x]$. Show that $f - Yg$ is irreducible in $K(y)[x]$.

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#abstract-algebra #ring-theory #principal-ideal-domains
272
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Why does Proposition 1.8 in Atiyah-Macdonald imply that the smallest prime $\mathfrak{p}$ containing a primary ideal is equal to its radical?

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#ring-theory #commutative-algebra
166
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Prove that a polynomial an irreducible g has no multiple root in C

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#ring-theory #factoring

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