What does $\cong$ sign represent? - Mathematics Stack Exchange 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 mapping known as an "isometry", which provides a formal definition of what "same shape and size" means) Two congruent triangles look exactly the same, but they are not the
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 . . . Originally you asked for $\mathbb {Z} (m) \otimes \mathbb {Z} (n) \cong \mathbb {Z} \text {gcd} (m,n)$, so any old isomorphism would do, but your proof above actually shows that $\mathbb {Z} \text {gcd} (m,n)$ $\textit {is}$ the tensor product
$\Bbb Z [i] (a+bi)\cong \Bbb Z (a^2+b^2)$ if $ (a,b)=1$. Gaussian . . . 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 $-1 \cong 10-1 \cong 9$ hence you get a well defined map $$\phi: \mathbb {Z} [i] \rightarrow B$$ by defining $\phi (a+bi):=a+3b$
linear algebra - Mathematics Stack Exchange 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