Where can I find an ontology of algebraic structures?

Question

• 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.

Answer 1

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

Answer 2

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.