IS $\mathbb Z_7$ an example of a commutative ring without zero-divisors that is not an integral domain?
I know it is has no zero divisors because it is prime, and that it is a field, but can someone help me understand integral domain?
2026-03-28 04:52:16.1774673536
Question about integral domains
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$\Bbb Z_7$ is a field, and every field is an integral domain.
On the other hand, every integral domain $D$ determines its field of fractions where fractions are formally built the same way as one constructs $\Bbb Q$ out of $\Bbb Z$.
We can also say that an integral domains $D$ contain the "integer elements" of its fraction field.
(And, as the example of $\Bbb Z_7$ (or, of any field) shows it is possible that all elements of a field are considered "integer" in this sense.)