Glossary of ring theory

Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation.

This is a glossary of some terms of the subject.

For ring-theoretic concepts in the language of modules, see also Glossary of module theory.

For specific types of algebras, see also: Glossary of field theory and Glossary of Lie groups and Lie algebras.

Since, currently, there is no glossary on not-necessarily-associative algebra structures in general, this glossary includes some concepts that do not need associativity; e.g., a derivation.