Symbols:D

Integral Domain

 * $D$

Used as a variable denoting the general integral domain.

Integral Domain as Algebraic Structure

 * $\struct {D, +, \circ}$

The full specification for an integral domain, where $+$ and $\circ$ are respectively the ring addition and ring product operations.

Ordered Integral Domain

 * $\struct {D, +, \circ, \le}$

This specifies an ordered integral domain which is totally ordered by the ordering $\le$.

Non-Zero Elements of Integral Domain

 * $D^*$

Let $\struct {D, +, \circ}$ be an integral domain whose zero is $0_D$.

Then $D^*$ denotes the set $D \setminus \set {0_D}$.

Non-Negative Elements of Ordered Integral Domain

 * $D_+$

Let $\struct {D, +, \circ, \le}$ be an ordered integral domain whose zero is $0_D$.

Then $D_+$ denotes the set $\set {x \in D: 0_D \le x}$, that is, the set of all positive (that is, non-negative) elements of $D$.

Positive Elements of Ordered Integral Domain

 * $D_+^*$

Let $\struct {D, +, \circ, \le}$ be an ordered integral domain whose zero is $0_D$.

Then $D_+^*$ denotes the set $\set {x \in D: 0_D < x}$, that is, the set of all strictly positive elements of $D$.

Some sources denote this as $D^+$, but this style of notation makes it difficult to distinguish between this and $D_+$.