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Number of ideals of norm $100$ of the Kleinian integers

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#algebraic-number-theory #normed-spaces #ideals #principal-ideal-domains #class-field-theory
49
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$\#ℤ[i]/\alpha\betaℤ[i] = \#ℤ[i]/\alphaℤ[i] · \#ℤ[i]/ \beta ℤ[i]$

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#abstract-algebra #ring-theory #ideals #gaussian-integers
99
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Simplifying Ideals to principal ideals

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#field-theory #algebraic-number-theory #ideals #finite-fields
306
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Elements of $\mathbb{R}[x]/f$ for polynomial $f$ of degree $n$

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#abstract-algebra #ring-theory #ideals #irreducible-polynomials
54
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On a special example of a Noetherian ring

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#commutative-algebra #modules #ideals
100
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On cardinality of generators

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#ring-theory #modules #ideals #cardinals
106
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Strange result on the nilradical $N(R)$ of a ring

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#abstract-algebra #ring-theory #ideals #noncommutative-algebra #nilpotence
151
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$\gcd \cdot \mathrm{lcm}$ in a commutative ring with zero divisors

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#abstract-algebra #ring-theory #ideals #gcd-and-lcm
397
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How to determine if an ideal is prime

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals
1.5k
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Show $\mathbb Z[x]/(x^2-cx) \ncong \mathbb Z \times \mathbb Z$.

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#abstract-algebra #ring-theory #ideals #polynomial-rings
153
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Why these are isomorphic each other for given these rings?

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#abstract-algebra #ring-theory #ideals
72
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In every local ring exist nonzero nilpotent ideals?

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#abstract-algebra #ring-theory #ideals #maximal-and-prime-ideals #nilpotence
69
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Product of the ideal and normal groups(Is this solution right?)

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#abstract-algebra #group-theory #ring-theory #ideals #solution-verification
91
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Find all maximal ideals of the ring $\mathbb Z[i]$ containing the ideal $I=(4-2i) \mathbb Z[i] + (9+3i) \mathbb Z[i]$

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#abstract-algebra #ideals
189
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If $I$ and $J$ are two ideals of a Lie algebra L then $(I+J)^{2n}\subset I^{n}+J^{n}$

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#abstract-algebra #ring-theory #lie-algebras #ideals #binomial-theorem

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