Uploaded September 2017 | Updated September 2026, 3 weeks ago

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The units in a ring are those elements which have an inverse under multiplication. They form a group, and this “group of units” is very important in algebraic number theory. Using units you can also define the idea of an “associate” which lets you generalize the fundamental theorem of arithmetic to all integers.

Definition of a Ring: bit.ly/2j4ZkMJ

Ring Examples: bit.ly/2tCAB5L

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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition
amzn.to/2oOBd5S

Milne, Algebra Course Notes (available free online)
jmilne.org/math/CourseNotes/index.html

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