Abstract Algebra/Manual of Style

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

Purpose

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

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

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

Chapter and section titles

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

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

With the exception of unimportant comments, each paragraph of text should be preceded with a "type declaration". Common types are Definition, Theorem, Lemma, Example, Note and Remark. A proof should be preceded 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

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).

There are no navigation templates.

Images

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.

Notation

Left = first usage, right = last usage

Groups: $G$
Elements of groups: $\sigma ,\tau ,\rho$
Subgroups: $H,K,I$
Elements of subgroups: $\eta ,\kappa ,\iota$
Normal subgroups: $N,M$
Normal series: $N_{1},\ldots ,N_{n}$ , $M_{1},\ldots ,M_{k}$
Generic integers: $n,k,m,l,j$
Summation indices: $j,k,n$
Sequence indices: $l,m$