Integers

A ring contains ℤ or ℤ𝑛

Let 𝑅 be a ring. Then 𝑅 has a unique subring isomorphic to Integers or modular arithmetic ℤ𝑛 ring given by the image of the unique homomorphism 𝐼 :ℤ →𝑅.

Proof

Since 𝐼(ℤ) ≅ℤ/ker⁡𝐼 and ker⁡𝐼 =𝑛ℤ where 𝑛 is the characteristic of 𝑅.

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