Ring theory is the branch of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

in which rings are studied: that is, structures supporting both an

addition Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol, +) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication, and Division (mathematics), divis ...

and a

multiplication Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division (mathematics), division. The result of a multiplication operation is called a ''Product (mathem ...

operation. This is a glossary of some terms of the subject. For the items in commutative algebra (the theory of commutative rings), see ''

Glossary of commutative algebra This is a glossary of commutative algebra. See also list of algebraic geometry topics, glossary of classical algebraic geometry, glossary of algebraic geometry, glossary of ring theory and glossary of module theory. In this article, all rings are ...

''. For ring-theoretic concepts in the language of modules, see also ''

Glossary of module theory Module theory is the branch of mathematics in which module (mathematics), modules are studied. This is a glossary of some terms of the subject. See also: ''Glossary of linear algebra'', ''Glossary of ring theory'', ''Glossary of representation the ...

''. For specific types of algebras, see also: ''

Glossary of field theory Field theory (mathematics), Field theory is the branch of mathematics in which field (mathematics), fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) De ...

'' 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.

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* * * * * * {{DEFAULTSORT:Glossary Of Ring Theory Ring theory Wikipedia glossaries using description lists