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Example of finite ring with a non principal ideal

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#abstract-algebra #ring-theory #finite-rings
42
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For $f, g \in K[t]$, $f \neq g$ implies $f_K \neq g_K$

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#polynomials #ring-theory
141
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Showing that an epimorphism of an ideal is again an ideal

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#abstract-algebra #ring-theory #ideals
211
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Irreducible elements and unique factorization domain

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#abstract-algebra #ring-theory #commutative-algebra #unique-factorization-domains
110
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For any $p,q\in\mathbb{Z}[i]$, $\mathrm{N}(\gcd(p, q))$ must divide $\gcd(\mathrm{N}(p), \mathrm{N}(q))$

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#abstract-algebra #ring-theory
81
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Confused about a solution: proving every prime ideal is maximal

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#abstract-algebra #ring-theory
316
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Solution verification: proving that $2$ is not prime in $\mathbb{Z}[\sqrt{-3}]$

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#abstract-algebra #ring-theory #solution-verification #maximal-and-prime-ideals
76
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To prove ; $pa:=a+a+... p $ times $=0 , \forall a \in R$ and $a^p=a , \forall a \in R$ for some prime $p$ then the ring $R$ is commutative

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#ring-theory #positive-characteristic
480
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Injective Ring Homomorphism

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#ring-theory #abstract-algebra
224
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Is is true that $R[x,y]/(x-y^2) \cong R[y]$?

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#abstract-algebra #ring-theory
1.3k
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If R is an integral domain disprove the RxR is an integral domain?

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#abstract-algebra #ring-theory
1k
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Where does the proof for commutative rings break down in the non-commutative ring when showing only two ideals implies the ring is a field?

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#abstract-algebra #ring-theory #commutative-algebra #noncommutative-algebra
152
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Minimal subring of complex numbers

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#abstract-algebra #ring-theory
3.7k
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Why $ \mathbb{Z}[x]$ is not Principal Ideal Domain

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#abstract-algebra #ring-theory #algebraic-number-theory
180
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MCS meet all prime ideals

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#abstract-algebra #ring-theory #commutative-algebra

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