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Noetherian ring of Krull dimension $0$

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#abstract-algebra #ring-theory #commutative-algebra #ideals
54
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Polynomial rings not useful when $R$ is a field?

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#ring-theory
2.1k
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Prove that a nonzero integer p is prime if and only if the ideal (p) is maximal in Z.

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
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Let R be a commutative ring with identity. Prove that R is a field if and only if (0R) is a maximal ideal.

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#abstract-algebra #ring-theory
1.1k
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Example of a finite ring with identity containing a ring without identity

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#abstract-algebra #ring-theory #finite-rings #rngs
5.5k
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Prove that R is a field.

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#abstract-algebra #ring-theory #proof-verification
170
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Is my proof for this completion of a ring not being flat correct?

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#ring-theory #commutative-algebra #proof-verification
361
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Krull's theorem and AC

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#abstract-algebra #ring-theory #set-theory
467
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Books on Rings without Identity

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#abstract-algebra #reference-request #ring-theory #noncommutative-algebra #rngs
68
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Showing that $\mathbb{Z}/2\mathbb{Z}[\mathbb{Z}/2\mathbb{Z}]$ is semi-simple

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#ring-theory
107
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Set or Ring, and group of units?

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#group-theory #ring-theory
900
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finite k-vector space noetherian

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#abstract-algebra #ring-theory #commutative-algebra #proof-verification
253
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Irreducible in $(\mathbb{Z}[i])[x]$

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#abstract-algebra #ring-theory #irreducible-polynomials
350
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Show an Ideal is the principal ideal for some polynomial.

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#polynomials #ring-theory #ideals
208
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Ideals and prime ideals in a commutative ring.

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#abstract-algebra #ring-theory #ideals

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