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Ring of remainders definition

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#abstract-algebra #ring-theory #integers #euclidean-domain
98
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Comparing orders induced by euclidean function and divisibility in euclidean domain

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#divisibility #order-theory #euclidean-domain
2.9k
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$\mathbb{Z}[i] / (2+3i)$ has 13 elements

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#abstract-algebra #proof-verification #ring-theory #ideals #euclidean-domain
988
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Dividing one polynomial by another

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#polynomials #fractions #euclidean-domain
72
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If the norm of $\alpha \in \mathbb{Z}[i]$ is a square, show that $\alpha$ is a square in $\mathbb{Z}[i]$

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#ring-theory #gaussian-integers #euclidean-domain
702
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Are 2x2 matrices on a Euclidean domain a Euclidean domain?

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#linear-algebra #ring-theory #gcd-and-lcm #euclidean-domain
142
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Showing that $\mathbb{Z}[\phi]$ is a UFD, where $\phi^2+\phi+1=0$.

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#abstract-algebra #ring-theory #commutative-algebra #euclidean-domain
208
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Maximizing the Euclidean Distance of a Constrained Sum

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#optimization #euclidean-domain
518
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Norm-Euclidean fields

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#euclidean-domain
330
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Showing $(3 + \sqrt{3})$ is not a prime ideal in $\mathbb{Z}[\sqrt{3}]$

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#abstract-algebra #proof-verification #euclidean-domain
3k
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Definition of a Euclidean domain

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#abstract-algebra #ring-theory #normed-spaces #principal-ideal-domains #euclidean-domain
181
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Why are irreducible elements prime in Euclidean domain?

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#abstract-algebra #ring-theory #euclidean-domain
421
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"Let $R$ be an integral domain. Assuming that the Division Algorithm holds in $R[x]$, prove that $R$ is a field."

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#abstract-algebra #group-theory #ring-theory #euclidean-domain
307
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Question about proof in Neukirch's Algebraic Number Theory

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#abstract-algebra #number-theory #algebraic-number-theory #euclidean-domain
120
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Is $\mathbb{R}[x^2,x^3]=\{f=\sum_{i=0}^n a_ix^i\in\mathbb{R}[x]:a_1=0\}$ is Euclidean Domain?

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#abstract-algebra #commutative-algebra #euclidean-domain

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