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Correlation between subring of Noetherian ring and submodule of Noetherian module

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#ring-theory #commutative-algebra #modules
557
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A prime ring with characteristic different from 2 is 2-torsion free.

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#ring-theory
505
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Noetherian prime localizations does not imply that whole ring is Noetherian

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#abstract-algebra #ring-theory #commutative-algebra
169
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irreducibility of polynomial over field of rational functions

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#abstract-algebra #ring-theory #field-theory #extension-field #irreducible-polynomials
416
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Non Noetherian ring with only one prime ideal

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#ring-theory #commutative-algebra
39
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What elements does a map of rings fix if both rings contain the same algebraically closed field as a subring?

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#abstract-algebra #ring-theory #field-theory #ring-homomorphism
53
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On Noetherian domains whose proper submodules of the fraction field are projective

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#ring-theory #commutative-algebra #modules #projective-module #integral-extensions
194
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When the element-wise product of two ideals produces an ideal

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#algebraic-geometry #polynomials #ring-theory #commutative-algebra #ideals
42
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A question about radical ideals

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#ring-theory #commutative-algebra #ideals
839
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Show that an ideal of the ring of integers of a real number field is not principal

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#number-theory #ring-theory #algebraic-number-theory #ideals #maximal-and-prime-ideals
452
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Equalizer in the category of rings with 1.

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#abstract-algebra #ring-theory #category-theory
384
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Finding a unique ring homomorphism

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#abstract-algebra #ring-theory #commutative-algebra #ring-homomorphism
136
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Semiprimitive rings and Modules

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#abstract-algebra #ring-theory #modules #radicals
840
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Is the polynomial $x^4+10x^2+1$ reducible over $\mathbb{Z}[x]$?

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#abstract-algebra #ring-theory #field-theory #irreducible-polynomials
2.2k
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The polynomial $x^6+x^3+1$ is irreducible over $\mathbb{Q}[x]$

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#abstract-algebra #ring-theory #field-theory #irreducible-polynomials

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