Symbols: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).

Totally Ordered Integral Domain
$$\left({D, +, \circ; \le}\right)$$

This specifies an 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 a Totally Ordered Integral Domain
$$D_+$$

Let $$\left({D, +, \circ; \le}\right)$$ be a totally 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 a Totally Ordered Integral Domain
$$D_+^*$$

Let $$\left({D, +, \circ; \le}\right)$$ be a totally 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_+^*.