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Ring theory
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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.
Quotes
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 A First Course in Noncommutative Rings http://books.google.com/books?id=f15FyZuZ3-4C&pg=PR9 21 June 2001 Springer Science & Business Media 978-0-387-95183-6 9
Quoted in Israel Kleiner A History of Abstract Algebra http://books.google.com/books?id=RTLRBK-wj6wC&pg=PA60 2 October 2007 Springer Science & Business Media 978-0-8176-4684-4 60
External links
Category:Mathematics