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Ring isomorphism for $k(G \oplus \mathbb Z )$ with $G$ torsion-free and abelian

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#ring-theory #field-theory #abelian-groups #group-rings #ring-isomorphism
39
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Regarding a ring isomorphism

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#abstract-algebra #polynomials #ring-theory #ring-isomorphism
422
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Showing isomorphism between two rings of fractions

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#abstract-algebra #ring-theory #fractions #localization #ring-isomorphism
733
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On ring isomorphism between cartesian products of rings

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#ring-theory #commutative-algebra #direct-product #ring-homomorphism #ring-isomorphism
287
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Explain why there is no subring of $\mathbb{Z}_{19}$ which is isomorphic to $\mathbb{Z}_{6}$.

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#abstract-algebra #ring-isomorphism
19.8k
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Example of an integral domain which is not a field

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#abstract-algebra #ring-theory #integral-domain #ring-isomorphism
132
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A false proof for the theorem about finite integral domains and fields

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#abstract-algebra #ring-theory #fake-proofs #integral-domain #ring-isomorphism
894
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Understanding the first isomorphism theorem for extension fields

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#abstract-algebra #polynomials #field-theory #galois-theory #ring-isomorphism
811
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Isomorphism in localization of rings

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#ring-theory #ideals #localization #ring-isomorphism
284
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If $A\simeq\prod A_i$ then $\sum e_i=1$

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#abstract-algebra #ring-theory #idempotents #ring-isomorphism
84
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If $I\lhd A$ then $M_n(A)/M_n(I) \simeq M_n(A/I)$

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#abstract-algebra #ring-theory #ring-isomorphism
410
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Units of Integers mod n

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#abstract-algebra #ring-theory #integers #group-isomorphism #ring-isomorphism
200
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Isomorphism Dual Numbers

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#polynomials #ring-theory #ring-isomorphism
67
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Proof $\Bbb{Z}[x]/(x-2) \cong \Bbb{Z}$?

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#abstract-algebra #ring-theory #ring-isomorphism
29
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Let $I=\langle 5,X^2+Y+1\rangle\subset R=\mathbb Z[X,Y]$. Show that $R/I\cong\mathbb F_5[X]$.

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#ideals #ring-isomorphism

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