Groupprops:Definition article

This article is part of the Groupprops Manual of Style
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This article is about a type of article on Groupprops

A definition article in Groupprops is mainly intended to provide a concise introduction to a particular term/notion, by describing its meaning, important properties, and its relation with other terms.

General information on definition articles

The default in Groupprops is: the article named after a term is the definition article for that term. In other words, if you check up the article on inner automorphism, you go to the definition article on inner automorphism. Thus, the article on a term is not:

A general survey of how the term came about
A study of the importance of the term or concept
A discussion about related ideas

The definition article does contain stuff other than the definitions and as such, would be reasonably encyclopaedic as far as all the information pertinent to the term is needed. However, it is not written in an encyclopaedic style.

For important terms (those which deserve separate discussion for motivation, importance etc.), there is usually a link on top, to a category listing all survey articles related to that term. These articles are in fact survey articles, written like professional essays, and exclusively dedicated to being reader-friendly.

Naming of the definition article

Further information: Groupprops:Term naming

Article-tagging templates

Definition articles (like other articles) begin with one or more article-tagging templates, that specify the theme, difficulty level, or property-theoretic type of the term being defined.

Further information: Groupprops:Definition article-tagging templates

Parts of the definition article

History section where the history of the term and the concept is briefly mentioned.
Definition section where the definition of the term may be given in different formats.
Study of this notion section which gives the sub-branch of the subject, as well as the mathematical subject classification for the notion defined.
References section where references to further articles on the topic may be given.
External links where web links/web references are given.

The remaining sections depend on the kind of term being defined. Typical kinds of terms are:

Properties for which we use the Property definition article format
Metaproperties for which we use the Metaproperty definition article format
Property operators for which we use the Property operator definition article format

Completeness rating for definition articles

Definition articles could be at any of the following stages of development:

Incomplete definition and/or incomplete article-tagging
Missing essential sections
Incomplete essential sections
Optional sections/subsections being developed

Incompleteness

A definition article is tagged as incomplete (via Template:Incomplete definition) if the definition itself is incomplete, or incorrect, in an important respect. If the term definition is correct, the definition article is not tagged as incomplete. Thus, the absence of a history section, references section, or external links section is not reason enough for the definition article to be termed incomplete.

Untagged articles or incompletely tagged articles

Each article should have article-tagging templates, which include the property-theoretic type specification template, the difficulty-level specification template, and other appropriate templates. Those articles which involve terms local to the templaet should employ Template:Wikilocal or a variation thereof. Articles without the proper templates are incompletely tagged.

Missing essential sections

Definition articles are supposed to have a history, references and external links section. They are also supposed to have article-tagging templates, and are supposed to have sections dependent on the kind of term being defined. A definition article where one or more of these sections is missing, even though the definition is itself complete, is at the missing essential sections stage.

Incomplete essential sections

Definition articles may have all the essential sections, but complete information may not be there in each section. For instance, the definition article on a group property may have a section titled Metaproperties but it may not have information on all the important metaproperties.

Partially developed optional sections

Optional sections are sections that are not part of the standard blueprint for that type of term but may be provided to convey additional information.

Optional sections include an Examples section, a section about Importance, a section on Testing or Computer Implementation.

Full fan-out

A good article is not only complete in itself, it also satisfies that all the articles it links out to are complete articles. For definition articles, we must check for the following:

All the links provided in the article-tagging templates are to existing pages
All the links provided in the definition are to existing pages. Thus, for instance, for a property definition article, the context over which the property is defined, should have a definition in the wiki.
All the links to stronger and weaker, and to related notions, should be available in the wiki
Proof links should be there for any implication relations, or for any property/metaproperty satisfactions

Quality rating for definition articles

The quality rating of a definition article depends on the following:

Its completeness rating, along the parameters defined above
Its accuracy rating: This is absorbed into the completness rating by our counting/measuring only the accurate content within the article
Its fluency and ease of understanding

Note that most of these concerns are very similar for other kinds of articles as well (viz fact articles, survey articles and articles about persons and other real-world entities).