Ring theory In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their r ...

is the branch of

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

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

addition Addition (usually signified by the plus symbol ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or '' sum'' ...

and a

multiplication Multiplication (often denoted by the Multiplication sign, cross symbol , by the mid-line #Notation and terminology, dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four Elementary arithmetic, elementary Op ...

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 ar ...

. 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 Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) Definition of a field A field is a commutative rin ...

and

Glossary of Lie groups and Lie algebras This is a glossary for the terminology applied in the mathematical theories of Lie groups and Lie algebras. For the topics in the representation theory of Lie groups and Lie algebras, see Glossary of representation theory. Because of the lack of o ...

. 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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References

* * * *Jacobson, Nathan (2009), Basic Algebra 1 (2nd ed.), Dover *Jacobson, Nathan (2009), Basic Algebra 2 (2nd ed.), Dover *Nathan Jacobson, Structure of Rings {{DEFAULTSORT:Glossary Of Ring Theory