ideal is principal. Bézout domains are a form of Prüfer domain. Any principal ideal domain (PID) is a Bézout domain, but a Bézout domain need not be a Noetherian...

mathematics, Bézout's identity (also called Bézout's lemma), named after Étienne Bézout who proved it for polynomials, is the following theorem: Bézout's identity — Let...

minor planet 17285 Bezout was named after him. Little Bézout's theorem Bézout's theorem Bézout's identity Bézout matrix Bézout domain O'Connor, John J.;...

integral domain is a Prüfer GCD domain if and only if it is a Bézout domain. If R is a non-atomic GCD domain, then R[X] is an example of a GCD domain that...

integral domain is a Bézout domain if and only if any two elements in it have a gcd that is a linear combination of the two. A Bézout domain is thus a...

is called a right Bézout ring. Left Bézout rings are defined similarly. These conditions are studied in domains as Bézout domains. A principal ideal...

integers is slightly more special than this: it is a Bézout domain. Let R be an integral domain with fraction field K. A fractional ideal is a nonzero...

ring is a local domain, and that every finitely generated ideal of a valuation ring is principal (i.e., a valuation ring is a Bézout domain). In fact, it...

over any unique factorization domain). A GCD domain (in particular, any Bézout domain or valuation domain). A Dedekind domain. A symmetric algebra over a...

elements Bézout domain, an integral domain in which the sum of two principal ideals is again a principal ideal Euclidean domain, an integral domain which...