Abstract Algebra/Manual of Style

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

Purpose[edit | edit source]

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 | edit source]

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 | edit source]

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

Chapter and section titles[edit | edit source]

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 | edit source]

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 | edit source]

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:


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

Definition 1: ...

Theorem 2: ...

Proof: ...

Remark 3: ...


Links[edit | edit source]

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).

Navigation[edit | edit source]

There are no navigation templates.

Images[edit | edit source]

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 | edit source]

All book chapters belong under the single category Book:Abstract Algebra

Notation[edit | edit source]

Left = first usage, right = last usage

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