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 re ...

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 Ring may refer to: * Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry * To make a sound with a bell, and the sound made by a bell :(hence) to initiate a telephone connection Arts, entertainment and media Film and ...

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), division. ...

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 additi ...

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 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 theory. A ...

. 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.

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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