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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
- What does the symbol $\\cong$ mean in the context of congruencies?
A symbol I have in my math homework looks like a ~ above a = (That is, $\\cong$ ) What does this mean? I'm studying Congruency at the moment if that helps
- 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 \
- 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
- $\\Bbb Z[i] (a+bi)\\cong \\Bbb Z (a^2+b^2)$ if $(a,b)=1$. Gaussian . . .
A very basic ring theory question, which I am not able to solve How does one show that Z[i] (3 − i) ≅Z 10Z Z [i] (3 − i) ≅ Z 10 Z Extending the result: Z[i] (a − ib) ≅Z (a2 +b2)Z Z [i] (a − i b) ≅ Z (a 2 + b 2) Z, if a, b a, b are relatively prime My attempt was to define a map, φ: Z[i] → Z 10Z φ: Z [i] → Z 10 Z and show that the kernel is the ideal generated
- 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
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