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If $R$ is Dedekind finite, then prove $_RR$ is Hopfian module.

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#abstract-algebra #ring-theory
395
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Existence of $n$ such that $a^n=a$ for all $a$ in $Z_m$

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#ring-theory #finite-rings
142
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Condition of coprime ideal

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#abstract-algebra #ring-theory
1.3k
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every integral domain has no non zero nilpotent

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#abstract-algebra #ring-theory #solution-verification
50
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Ring in which Jacobson Radical is different from nil radical

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#ring-theory #commutative-algebra
1.1k
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Example of Ring Homomorphism such that inverse image of maximal ideal is not maximal.

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#ring-theory #commutative-algebra
39
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Question about Ring of Fractions

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#ring-theory
63
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Field of Fractions of a Field

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#ring-theory #field-theory
134
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Prove that $\text{Frac}(\mathbb{Z}[\sqrt{d}]) \cong \mathbb{Q}(\sqrt{d})$

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#abstract-algebra #ring-theory #field-theory
100
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About condition of The Incomparability theorem

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#abstract-algebra #ring-theory
158
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Simple examples of rings with non-trivial Picard group and infinite Brauer group

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#algebraic-geometry #ring-theory #commutative-algebra #examples-counterexamples #big-list
59
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What is the submodule of $M \otimes_R N$ generated by $1 \otimes_R n$?

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#abstract-algebra #ring-theory #tensor-products
280
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Proving Division Rings of $p^2$ Elements are Fields

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#abstract-algebra #ring-theory #solution-verification #division-ring
62
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Ring whose every simple singular module is faithful.

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#ring-theory #modules
120
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Question on Primitive Ring and $\operatorname{End}(V)$

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#abstract-algebra #ring-theory #soft-question #modules

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