O'Reilly logo

The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

III.81 Rings, Ideals, and Modules

1 Rings

A ring, like a GROUP [I.3 §2.1] or a FIELD [I.3 §2.2], is an algebraic structure that satisfies certain axioms. To remember the axioms for both rings and fields at the same time, it is helpful to think of two simple examples: with the two operations of addition and multiplication, the set Image of all integers forms a ring and the set Image of all rational numbers forms a field. In general, a ring is a set R with two BINARY OPERATIONS [I.2 §2.4], denoted by “+” and “×”, which satisfies all the field axioms apart ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required