# Symbols:D

## Contents

## deci-

- $\mathrm d$

The Système Internationale d'Unités symbol for the metric scaling prefix **deci**, denoting $10^{\, -1 }$, is $\mathrm { d }$.

Its $\LaTeX$ code is `\mathrm {d}`

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## deka-

- $\mathrm {da}$

The Système Internationale d'Unités symbol for the metric scaling prefix **deka**, denoting $10^{\, 1 }$, is $\mathrm { da }$.

Its $\LaTeX$ code is `\mathrm {da}`

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## Hexadecimal

- $\mathrm D$ or $\mathrm d$

The hexadecimal digit $13$.

Its $\LaTeX$ code is `\mathrm D`

or `\mathrm d`

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## Roman Numeral

- $\mathrm D$ or $\mathrm d$

The Roman numeral for $500$.

Its $\LaTeX$ code is `\mathrm D`

or `\mathrm d`

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## 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.

Its $\LaTeX$ code is `\struct {D, +, \circ}`

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## Ordered Integral Domain

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

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

Its $\LaTeX$ code is `\struct {D, +, \circ, \le}`

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## 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 $D \setminus \set {0_D}$.

Its $\LaTeX$ code is `D^*`

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## 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 $D$.

Its $\LaTeX$ code is `D_+`

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## 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 $D_+$.

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

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