A ring contains $ℤ$ or $ℤ 𝑛$

Let $𝑅$ be a ring. Then $𝑅$ has a unique subring isomorphic to $ℤ$ or modular arithmetic $ℤ 𝑛$ #m/thm/ring given by the image of the unique homomorphism $𝐼 : ℤ \to 𝑅$ .

Proof

Since $𝐼 (ℤ) ≅ ℤ / k e r 𝐼$ and $k e r 𝐼 = 𝑛 ℤ$ where $𝑛$ is the characteristic of $𝑅$ .

#state/tidy | #lang/en | #SemBr

A ring contains ℤ or ℤ𝑛

A ring contains $ℤ$ or $ℤ 𝑛$