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Prove, that if the commutative ring has no zero divisors, then it is a field

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#abstract-algebra #ring-theory #commutative-algebra
135
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Determine the center of ring of differential operators with coefficients in $\mathbb{C}[z_1,z_2]$

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#polynomials #ring-theory
31
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Element in distinct prime ideal

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#ring-theory #dedekind-domain
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$\mathbb{Z}\bigl[1+\sqrt{-7}\bigr]$ is not Euclidean

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#abstract-algebra #ring-theory
139
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Tensor product of quotient and kernel

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#abstract-algebra #ring-theory #commutative-algebra #principal-ideal-domains
146
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finitely generated subgroup of $\mathbb{Q}^n$

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#linear-algebra #abstract-algebra #group-theory #ring-theory
4k
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Can the complex numbers be realized as a quotient ring?

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#abstract-algebra #ring-theory
215
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Find a "simpler description" for $\mathbb{Z}[X]/(X-5,X^2+3)$

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#abstract-algebra #ring-theory
161
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A nonprincipal ideal and a nonprime irreducible in $\mathbb{Z}[\sqrt{-17}]$

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#abstract-algebra #ring-theory #algebraic-number-theory
216
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meadows and fields, aren't $0^{-1}=0$ can be proven simply from the axioms of fields?

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#abstract-algebra #ring-theory #field-theory
593
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Zero dimensional Gorenstein ring

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#ring-theory #commutative-algebra #homological-algebra #gorenstein
341
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Any finite integral domain is a field

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#abstract-algebra #ring-theory
185
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How to find algebraic connections between zeros of a polynomial?

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#group-theory #polynomials #ring-theory #galois-theory
298
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Can $\operatorname{Spec}(A)$ be expressed as an inverse limit?

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#general-topology #ring-theory #commutative-algebra
235
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Representation of Algebraic Extensions by Matrices

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#abstract-algebra #ring-theory #field-theory

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