# Ring theory

Branch of algebra

In abstract 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.

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## QuotesEdit

- Today, ring theory is a fertile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential operators, invariant theory), arithmetic (orders, Brauer groups), universal algebra (varieties of rings), and homological algebra (cohomology of rings, projective modules, Grothendieck and higher K-groups).
- Tsit-Yuen Lam (21 June 2001).
*A First Course in Noncommutative Rings*. Springer Science & Business Media. p. 9. ISBN 978-0-387-95183-6.- Quoted in Israel Kleiner (2 October 2007).
*A History of Abstract Algebra*. Springer Science & Business Media. p. 60. ISBN 978-0-8176-4684-4.

- Quoted in Israel Kleiner (2 October 2007).

- Tsit-Yuen Lam (21 June 2001).