Ring theory MOC

GCD

Let be an integral domain and . An element is a greatest common divisor or GCD of and iff ring

and implies .¹ The GCD is unique up to associate elements, leading to the abuse of notation

Properties

1. GCDs exist for nonzero elements in a UFD

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Footnotes

1. 2009. Algebra: Chapter 0, §V.2.1, p. 252 ↩