Ring theory

Inabstract algebra,ring theoryis the study ofrings—algebraic structuresin which addition and multiplication are defined and have similar properties to those operations defined for theintegers.

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Quotes

Today, ring theory is a fertile meeting ground forgroup 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), andhomological algebra(cohomology of rings, projective modules,Grothendieckand 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 inIsrael Kleiner (2 October 2007).A History of Abstract Algebra.Springer Science & Business Media. p. 60.ISBN 978-0-8176-4684-4.

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Ring theory

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