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- What does $\cong$ sign represent? - Mathematics Stack Exchange
I came across this sign when reading some papers I looked up Wikipedia It says "The symbol "$\\cong$" is often used to indicate isomorphic algebraic structures or congruent geometric figures "
- Difference between ≈, ≃, and ≅ - Mathematics Stack Exchange
In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical Operators B
- Proof of $(\\mathbb{Z} m\\mathbb{Z}) \\otimes_\\mathbb{Z} (\\mathbb{Z . . .
I've just started to learn about the tensor product and I want to show: $$ (\mathbb {Z} m\mathbb {Z}) \otimes_\mathbb {Z} (\mathbb {Z} n \mathbb {Z}) \cong \mathbb
- abstract algebra - If $\mathbb Q \otimes_\mathbb Z \mathbb Q \cong . . .
In Dummit Foote, it is an exercise to show that $\mathbb Q \otimes_\mathbb Z \mathbb Q$ is a $1$-dimensional $\mathbb Q$-vector space This is fairly easy: a $\mathbb Q$-basis for $\mathbb Q \
- Let - Mathematics Stack Exchange
Let M M and N N be two normal subgroups of G G Show that M ∩ N M ∩ N is also normal in G G Furthermore,if G = MN G = M N then show that
- abstract algebra - How to show that $ {_R}M \otimes_R {_R}N \cong {_R . . .
This is a duplicate question But to give you a hint already: Don't show injectivity Construct an inverse map Recall that an isomorphism is an invertible homomorphism This is the best, useful, scalable and easy definition of an isomorphism Forget about injective and surjective, this is a lemma, not a definition
- $\\hom (M, \\coprod_i N_i) \\cong \\bigoplus_i \\hom (M, N_i)$ in . . .
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 it? Instead, you can save this post to reference later
- abstract algebra - Prove that Aut ($\mathbb Z \times \mathbb Z$) $\cong . . .
Prove that Aut ($\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 problem on math SE, however
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