UFD

Noun

Meaning

UFD (plural UFDs)

(algebra) Initialism of unique factorization domain.

Synonyms

Examples

A Bézout domain is thus a GCD domain, and (4) gives yet another proof that a PID is a UFD. Source: Internet

Also, a Dedekind domain is a UFD if and only if its ideal class group is trivial. Source: Internet

Any Euclidean domain is a unique factorization domain (UFD), although the converse is not true. Source: Internet

By iteration, a polynomial ring in any number of variables over any UFD (and in particular over a field) is a UFD. Source: Internet

Equivalent conditions for a ring to be a UFD A Noetherian integral domain is a UFD if and only if every height 1 prime ideal is principal (a proof is given below). Source: Internet

For example, it follows immediately from (2) that a PID is a UFD, since, in a PID, every prime ideal is generated by a prime element. Source: Internet

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