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Jul 1, 2016 · A homework problem asked to find a short exact sequence of abelian groups $$0 \rightarrow A \longrightarrow B \longrightarrow C \rightarrow 0$$ such that $B \cong A \oplus …
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This approach uses the chinese remainder lemma and it illustrates the 'unique factorization of ideals' into products of powers of maximal ideals in Dedekind domains: It follows $-1 \cong 10 …
You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I get …
Oct 4, 2016 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation …
Nov 20, 2017 · I am trying to show the above result. First, I compute that the Minkowski bound must be strictly lower than 4. Therefore, for every ideal class, there is a representative, so that …
Nov 26, 2014 · How can I see that the connected sum $\mathbb {P}^2 \# \mathbb {P}^2$ of the projective plane is homeomorphic to the Klein bottle? I'm not necessarily looking for an explicit …
Feb 23, 2023 · 1 Prove that Aut ($\mathbb Z \times \mathbb Z$) $\cong$ $\text {GL}_2 (\mathbb Z)$. This is a HW problem for an Algebra course, hints/suggestions welcome. I didn't find this …
In geometry, $\cong$ means congruence of figures, which means the figures have the same shape and size. (In advanced geometry, it means one is the image of the other under a …
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