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 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'' of ...
and a
multiplication
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being ad ...
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. 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 ring ...
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 ...
. 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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See also
*
Glossary of module theory
Notes
References
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*
*
*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
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 ...