Symbols:D

Hexadecimal

$\mathrm D$ or $\mathrm d$

The hexadecimal digit $13$.

Its $\LaTeX$ code is \mathrm D or \mathrm d.

Integral Domains

$D$

Used as a variable denoting the general integral domain.

Integral Domain as an Algebraic Structure

$\left({D, +, \circ}\right)$

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

Its $\LaTeX$ code is \left({D, +, \circ}\right).

Ordered Integral Domain

$\left({D, +, \circ, \le}\right)$

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

Its $\LaTeX$ code is \left({D, +, \circ, \le}\right).

Non-Zero Elements of an Integral Domain

$D^*$

Let $\left({D, +, \circ}\right)$ be an integral domain whose zero is $0_D$.

Then $D^*$ denotes the set $D - \left\{{0_D}\right\}$.

Its $\LaTeX$ code is D^*.

Non-Negative Elements of an Ordered Integral Domain

$D_+$

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

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

Its $\LaTeX$ code is D_+.

Positive Elements of an Ordered Integral Domain

$D_+^*$

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

Then $D_+^*$ denotes the set $\left\{{x \in D: 0_D < x}\right\}$, 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 $D_+$.

Its $\LaTeX$ code is D_+^*.