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$\mathbb{Z}[i]/(1+i) \cong \mathbb{Z}/\mathbb{2Z}$

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#ring-theory
872
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Show that the polynomial ring in $n-1$ variables is isomorphic to the polynomial ring in one variable $x_{n}$

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#abstract-algebra #ring-theory #graph-isomorphism
1.3k
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Transfer Between LCM, GCD for Rings?

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#abstract-algebra #ring-theory
253
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Want to prove that some $\mathbb R[x]$-Module has no basis

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#abstract-algebra #polynomials #ring-theory
129
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Problem related to prime ideals of B and A where B is integral over A

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#abstract-algebra #commutative-algebra #ring-theory
269
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Ring isomorphisms maintain noetherian property?

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#abstract-algebra #ring-theory #noetherian
99
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Annihilator of $a'$ and $b'$ in the ring $\mathbb{Z}/(a'b')$ ?

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#ring-theory #ideals
90
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Showing that $R$ is an ID with $0$ and $P$ only prime ideals.

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#ring-theory
61
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How can we show that $\operatorname{Tor}_1^A(\hat{A},G_f/G)=0$?

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#abstract-algebra #commutative-algebra #ring-theory #modules #tensor-products
112
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Prime Ideals as Ring theoretic Ultrafilters

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#algebraic-geometry #ring-theory #category-theory
8.2k
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About the ring $\{a+b\sqrt{2}\mid a,b\in \Bbb Z\}$

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#abstract-algebra #ring-theory
636
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Reducibility of a Cyclotomic Polynomial under the ring homomorphism $\mathbb{Z} \rightarrow \mathbb{F}_p$

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#polynomials #ring-theory #field-theory #galois-theory #irreducible-polynomials
642
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Is this matrix decomposition possible?

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#linear-algebra #matrices #ring-theory
562
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Ascending chain of ideals

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#ring-theory
182
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$\mathbb{Z}_6[x]$/$\langle2x-3\rangle$ isomorphic to what?

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#abstract-algebra #ring-theory

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