Definition:Strict Positivity Property

Definition
Let $\struct {R, +, \times}$ be a ring upon which a property $P$ can be applied to a subset of $R$ as follows:

The property $P$ is called the strict positivity property.

Also known as
This is usually known in the literature as the positivity property.

However, this is also used to define a similar property such that $\map P {0_R}$.