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Describe free commutative algebra on a set X.

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#abstract-algebra #ring-theory
50
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Is the product of finitely many Noetherian rings itself noetherian?

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#ring-theory
721
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An isomorphism between fields of fractions

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#abstract-algebra #ring-theory
196
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Isomorphic Factor Rings of Z_2[x]

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#abstract-algebra #ring-theory #field-theory #ideals #finite-fields
37
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Prove that $f(R) = \{ y \in P\ | \; (\exists x \in R)\; f(x) = y \; \} $ is a subring of ring $P$.

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#abstract-algebra #ring-theory
238
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infinite product of finite Noetherian rings

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#abstract-algebra #ring-theory
256
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A set of elements in a reduced unity ring

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#abstract-algebra #ring-theory #contest-math
90
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Can we say that the following diagram is commutative?

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#abstract-algebra #ring-theory #commutative-algebra #category-theory #modules
65
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Smallest element in unit group

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#abstract-algebra #group-theory #ring-theory
321
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Show ideal generated by unit times element is the same as ideal generated by element

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#abstract-algebra #ring-theory #ideals
350
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How can I show that $\mathbb R [x]/(x^5+x-3)$ is not an Integral domain?

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#polynomials #ring-theory #integral-domain
125
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Verify my solution - simple right submodule of Weyl algebra is inifnite dimensional as complex vector space.

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#linear-algebra #abstract-algebra #ring-theory #noetherian
68
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Is the homomorphism induced on symmetric algebras injective?

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#abstract-algebra #ring-theory #commutative-algebra #modules
106
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Which ring is $R[X,Y,Z,T]/(X-Y^2,T-Y^4,T^3-Z)$ isomorphic to?

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#abstract-algebra #ring-theory
133
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Ideal of upper triangular matrices over non noetherian ring.

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#matrices #ring-theory #ideals #noetherian

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