• A group is a monoid where every element admits an inverse,
  • A ring is a monoid under multiplication that distributes over a commutative group
  • A field is a ring whose non-zero elements form a group under multiplication
  • and so on...

These type of relationships form an ontology of algebraic structures. Is there a formal ontology of mathematics available somewhere, perhaps in the OWL/RDF format?

edit: to give you an idea of the motivation, it would be nice to automatically extract dependency graph for an algebraic structure. I quickly drew an (incomplete) one for an Abelian variety.

  • $\begingroup$ What do you mean by ontology here? What about en.wikipedia.org/wiki/Algebraic_structure or en.wikipedia.org/wiki/List_of_algebraic_structures ? $\endgroup$ Commented Jul 1, 2014 at 12:46
  • $\begingroup$ I provided a link that describes what I mean by ontology. These two Wikipedia article are a good start, but I'm looking for something much deeper. For instance, can you tell me, offhand, from the list what are all the structures involved in describing an Abelian variety? $\endgroup$
    – Arthur B.
    Commented Jul 1, 2014 at 13:01
  • $\begingroup$ I am not sure that this question leads to something deep, as you say. The "graph" for an abelian variety is nice (but not deep). $\endgroup$ Commented Jul 1, 2014 at 18:19
  • $\begingroup$ I mean "deep" in the sense of "thorough", not "profound". My Abelian Variety graph isn't thorough at all. $\endgroup$
    – Arthur B.
    Commented Jul 1, 2014 at 18:27

2 Answers 2


Please take a look at our OntoMathPro, a crowdsourced ontology of professional-level mathematics, covering a wide range of topics including algebra.

  • $\begingroup$ How are the classes related? For example just tells you a single direction, not how, and is without reference to the smaller components that make up the class. $\endgroup$
    – multicusp
    Commented Aug 21, 2019 at 0:59

I have two similar graphs at pages 1 and 24 of my BSc thesis.

One online resource listing many algebraic structures by their properties is MathStructures on chapman.edu.

Also, Groupprops for the group-like structures.


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