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Special representatives for elements of a quotient ring

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#ring-theory #commutative-algebra #ideals
126
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Product of algebraic numbers

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#abstract-algebra #ring-theory
71
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Example of a ring $R$ and a prime $0\neq P\unlhd R$ such that $R_P$ is a field?

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#ring-theory #commutative-algebra #maximal-and-prime-ideals #localization
91
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Quotienting by the Leading Term Ideal

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#abstract-algebra #reference-request #ring-theory #commutative-algebra #groebner-basis
1.3k
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Is the set of upper(and separately lower)-triangular matrices a ring?

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#abstract-algebra #matrices #ring-theory
52
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Left divisors are right divisors in an algebra where every element is algebraic

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#linear-algebra #abstract-algebra #ring-theory
53
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Sharp's Exercise 13.35

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#ring-theory #integral-extensions
785
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Is the ideal $I:=\langle xy-z,x^5-z^3 \rangle $ prime in $\Bbb{C}[x,y,z]$?

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#abstract-algebra #ring-theory #irreducible-polynomials #maximal-and-prime-ideals
369
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Proving a subring has only one maximal ideal.

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#abstract-algebra #ring-theory
1.1k
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Is the ideal $J:=\langle -y^2+xz,x^5-z^3 \rangle$ prime in $\Bbb{C}[x,y,z]?$

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#abstract-algebra #algebraic-geometry #ring-theory #maximal-and-prime-ideals #multivariate-polynomial
442
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Subrings of localizations

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#abstract-algebra #ring-theory #commutative-algebra #localization
1k
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Inner product in module theory

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#ring-theory #commutative-algebra #modules #inner-products #projective-module
83
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Convergence properties in a Hausdorff space that is a ring

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#general-topology #ring-theory #convergence-divergence #hausdorff-distance
389
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Arbitrary Ring and Field Contruction

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#abstract-algebra #group-theory #ring-theory #field-theory
98
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On the subring $k + Y k [X,Y]$ of the polynomial ring $k[X,Y]$

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#ring-theory #commutative-algebra #krull-dimension #integral-extensions

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