< back to index

Integral domain (ID)

Definition

An integral domain is a commutative ring that has no zero-divisors.

Properties

If $I,J \subseteq R$ are non-zero ideals, then their intersection is non-zero. To show this, take non-zero elements $i \in I, j \in J$ and then $ij \in I \cup J \setminus \{0\}$.

An integrable domain is a torsion-free module over itself.

all these pages adapted with probably insufficient credit from my university's lecture notes