MathGloss

Let RR be a commutative ring and let a,bRa,b\in R. An element dRd\in R is a greatest common divisor of aa and bb if dd divides aa and dd divides bb and for every dRd’\in R such that dd’ divides aa and dd’divides bb, we have that dd’ divides dd.

Equivalently, dd is a greatest common divisor of aa and bb if the ideal generated by dd is the smallest principal ideal that contains both aa and bb. This ideal is unique.

Wikidata ID: Q131752