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15
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$K=F(\alpha)$ if $K$ is a quadratic extension

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#abstract-algebra #ring-theory #field-theory #galois-theory #extension-field
214
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Corollary 15.3.8 from Artin (degrees of field extensions)

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#abstract-algebra #ring-theory #field-theory #galois-theory #extension-field
376
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Which of the following quotient rings is not a field?

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#abstract-algebra #ring-theory #field-theory
1.1k
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Endomorphism ring of infinite dimensions vector space

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#abstract-algebra #ring-theory #modules #noncommutative-algebra
734
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Ring of Invariants of $A_3$

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#abstract-algebra #group-theory #ring-theory #invariant-theory
193
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Is $\mathbb{Z}[x]/(5x)$ isomorphic to $\mathbb{F}_5[x]$?

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#abstract-algebra #polynomials #ring-theory #field-theory
35
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$dim(R / fR) = dim(R) -1$ if $f$ Regular

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#ring-theory #commutative-algebra
300
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Isomorphism of dual and regular representation of matrix algebra $A$

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#abstract-algebra #ring-theory #representation-theory
247
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Local Units and Enough Idempotents

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#ring-theory
41
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How to show that the annihilating-ideal graph $AG(R)$ is an empty graph if and only if $R$ is an integral domain?

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#abstract-algebra #graph-theory #ring-theory
54
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Defining various types of multiplication in rings

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#abstract-algebra #ring-theory
61
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Proving that maximally non-finitely generated ideals of a commutative ring are prime.

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#abstract-algebra #ring-theory #commutative-algebra
55
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Proving that $\frac{R[x]}{I[x]} \cong \frac{R}{I} [x]$

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#abstract-algebra #polynomials #ring-theory
1.9k
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What are the units of $\mathbb Z/2\mathbb Z \times \mathbb Z/5\mathbb Z$

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#abstract-algebra #group-theory #ring-theory #cyclic-groups #direct-product
59
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The isomorphic between rings

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#ring-theory #group-rings

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