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Associates of (x + 1) in Q[x]

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#abstract-algebra #ring-theory
53
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Successive quotients of powers of a non-zero prime ideal in Dedekind domain

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#abstract-algebra #ring-theory #dedekind-domain
246
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Maximal ideal among those that are not finitely generated

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#abstract-algebra #ring-theory #commutative-algebra #ideals
174
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Is the following ring (artinian) semisimple? And are any of these attempts valid?

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#abstract-algebra #ring-theory #modules #artinian #semi-simple-rings
90
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I look for 2 commutative algebra counterexamples

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#abstract-algebra #ring-theory #commutative-algebra #tensor-products #noetherian
44
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Why $(r+(p))(a+pA) = ra+pA$ holds?

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#abstract-algebra #ring-theory #modules
85
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Proving cardinality of basis in Module theory

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#abstract-algebra #ring-theory #modules
1.3k
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Which elements of $\mathbb Z \times \mathbb Z$ are zero divisors?

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#abstract-algebra #ring-theory
68
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What does 5 equal in $Z[i]$

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#abstract-algebra #ring-theory
139
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Describe the kernel of the following map

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#abstract-algebra #ring-theory
75
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Showing an ideal is prime

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals #ring-isomorphism
74
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Understanding why complicated argument is necessary when looking for index 2 subgroups

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#group-theory #ring-theory #ordered-fields
109
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multiplication of a ring subsets

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#abstract-algebra #ring-theory
132
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Is $3 − 2i$ irreducible in $\mathbb Z[i]$?

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#abstract-algebra #ring-theory
1k
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Prove that if $R$ and $S$ are rings, $\theta : R \to S$ is an isomorphism, and $e$ is a unity of $R$, then $\theta (e)$ is a unity of $S$

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#abstract-algebra #group-theory #ring-theory #group-isomorphism

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