Ring of integers
This article is about a particular ring, i.e., a ring unique up to isomorphism. View a complete list of particular rings
Definition
The ring of integers, denoted , is the set of integers with addition and multiplication defined as for ordinary integers.
Ring properties
Basic properties
| Property | Satisfied? | Explanation |
|---|---|---|
| integral domain | Yes | |
| unique factorization domain | Yes | Fundamental Theorem of Arithmetic |
| principal ideal domain | Yes | |
| Euclidean domain | Yes | |
| field | No | No inverse of e.g. |
