Integrity Ring

algebra

Definition

Integritätsring

Integrity Ring

A commutative ring with 1 without zero divider is called integrity ring.

Simplifcation Rule

A benefit of working in an integrity ring is that the following simplification rule applies:

$$\begin{array}{r}a\cdot b=a\cdot c\wedge a\ne 0⟹b=c\end{array}$$