# Abstract Algebra/Manual of Style

This section defines the style rules that should be applied throughout the Abstract Algebra wikibook.

## Contents

## Purpose[edit]

This is intended as a University-level textbook for students of mathematics. Readers are therefore expected to be familiar with math fundamentals, and with the material in the Algebra and Linear Algebra wikibooks.

## Language[edit]

The style of the language should be that of an ordinary math textbook: clear and precise but without talking down to the reader. Personal comments should be avoided.

The book should use standard American English spelling throughout.

## Structure[edit]

Each page should read like a section of a paper textbook, with external links to futher reading where appropriate.(?)

## Chapter and section titles[edit]

For top-level chapter titles, all words should be capitalised apart from articles and prepositions (e.g. "Equivalence Relations and Congruence Classes"). Sub-headings within a page should only have the first letter of the heading capitalised.

## Page length restrictions[edit]

There are no additional page length restrictions imposed by this style guide, but do follow the global Wikibooks convention of limiting page lengths at 35k (?)

## Templates[edit]

With the exception of unimportant comments, each paragraph of text should be preceeded with a "type declaration". Commen types are *Definition*, *Theorem*, *Lemma*, *Example*, *Note* and *Remark*. A proof should be preceeded with the word "*Proof*" in italics and a semicolon, and ended with a black square: ∎ . Code:

{{Unicode|∎}}

The same counter should be used for all types of paragraphs. Example:

**Definition 1:** ...

**Theorem 2:** ...

*Proof*: ... ∎

**Remark 3:** ...

etc...

## Links[edit]

Don't link outside the book (except in the introduction to the book as a whole, which can link to other books that are prerequisites).

## [edit]

There are no navigation templates.

## Images[edit]

All images should be in Wikimedia commons. Since the vast majority of images will be diagrams to illustrate a point in the surrounding text, thumbnails will probably not be appropriate.

## Categories[edit]

All book chapters belong under the single category Abstract Algebra

## Notation[edit]

Left = first usage, right = last usage

- Groups:
- Elements of groups:
- Subgroups:
- Elements of subgroups:
- Normal subgroups:
- Normal series: ,
- Generic integers:
- Summation indices:
- Sequence indices: