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What is a generator for an ideal such that $I=\{a+bi|a+b \text{ is even}\}$?

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#ring-theory #modular-arithmetic #ideals #gaussian-integers #parity
134
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prove that a set is a domain

Published on
#polynomials #ring-theory
148
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Ideals in $R$ and $R[x]$

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#ring-theory #polynomial-rings
134
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non-zero non-invertible polynomial implies zero divisior

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#abstract-algebra #polynomials #ring-theory
28
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Prove that $Z_l \left( K \left[ t,t^{-1} \right]\right)=0$.

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#abstract-algebra #polynomials #ring-theory
56
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Determine the minimal polynomial over different fields

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#abstract-algebra #polynomials #ring-theory
48
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Primes containing a fixed element $f$ in a finitely generated $k$-algebra.

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#algebraic-geometry #ring-theory #commutative-algebra #maximal-and-prime-ideals
42
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Associates in rings that differ by more than sign

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#abstract-algebra #ring-theory
31
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quotient ring (R/I) has multiplicative identity but R does not

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#abstract-algebra #ring-theory #quotient-group
71
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Is $D^{-1}R$ regular?

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#abstract-algebra #ring-theory #commutative-algebra #localization #regular-rings
115
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Motivation for Application of Dedekind-Hasse Norm

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#abstract-algebra #ring-theory
498
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Find all ideals of $\mathbb{Z}_n$

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#abstract-algebra #ring-theory #modular-arithmetic #ideals
31
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Comparing the exactness of $(\prod_{\lambda\in \Lambda}M_{\lambda})$ and $M_{\lambda}$ on a long exact sequence.

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#ring-theory #modules #homology-cohomology #exact-sequence #injective-module
2.7k
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Show that $\mathbb{Z}[x]/(x)$ is isomorphic to $\mathbb{Z}$

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#abstract-algebra #ring-theory #ideals #group-isomorphism
487
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Showing that $\mathbb{Z}[x]/_{(x)}$ is isomorphic to $\mathbb{Z}$

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

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