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A non-zero ring $R$ is a field if and only if for any non-zero ring $S$, any ring homomorphism from $R$ to $S$ is injective.

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#abstract-algebra #proof-verification #ring-theory
789
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Group of units of ring of formal power series

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#abstract-algebra #ring-theory
1.3k
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How to find all irreducible elements in $\mathbb{Z}[\sqrt{2}]$

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#abstract-algebra #ring-theory
333
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Formal power series and ideals

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#abstract-algebra #ring-theory
170
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Computing generators of polynomial rings (software/algorithm)

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#polynomials #ring-theory #algorithms #math-software
60
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How can I show $\sqrt{2-\sqrt{2}} \in \mathbb Q\Big(\sqrt{2+\sqrt{2}}\Big)$?

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#abstract-algebra #ring-theory #field-theory #extension-field
59
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check whether $5$ is irreducible in $\Bbb{Z}[\sqrt{-2}]$

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#abstract-algebra #ring-theory
41
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Isomorphism between submodules as one-sided ideals

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#abstract-algebra #ring-theory #ideals #noncommutative-algebra
217
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What is meant by 'scalars in modules'?

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#ring-theory #field-theory #modules #scalar-fields
67
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Nilpotent element $a^2$ in a polynomial quotient ring

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#abstract-algebra #ring-theory #ideals #irreducible-polynomials
22
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Understanding a ring homomorphism

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#abstract-algebra #ring-theory
27
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Can we find a basis $B$ of $M$ such that $|B|=1$?

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#abstract-algebra #matrices #ring-theory #modules
4.4k
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Finding all the ideals of $\mathbb{Z} [x]/(2, (x^3+1))$?

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#abstract-algebra #ring-theory #quotient-spaces #polynomial-rings
125
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Why is $(J : I ) = \{x \in R\mid xI \subset J \}$ an ideal?

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#abstract-algebra #ring-theory
131
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Proof of polynomial division theorem

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#abstract-algebra #polynomials #ring-theory #proof-explanation

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