Unique Factorization Domain
In mathematics, a unique factorization domain (UFD) is a commutative ring in which every non-unit element, with special exceptions, can be uniquely written as a product of prime elements (or irreducible elements), analogous to the fundamental theorem of arithmetic for the integers. UFDs are sometimes called factorial rings, following the terminology of Bourbaki.
Note that unique factorization domains appear in the following chain of class inclusions:
- Commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields
Read more about Unique Factorization Domain: Definition, Examples, Non-examples, Properties, Equivalent Conditions For A Ring To Be A UFD
Famous quotes containing the words unique and/or domain:
“The parent must not give in to his desire to try to create the child he would like to have, but rather help the child to develop—in his own good time—to the fullest, into what he wishes to be and can be, in line with his natural endowment and as the consequence of his unique life in history.”
—Bruno Bettelheim (20th century)
“In the domain of art there is no light without heat.”
—Victor Hugo (1802–1885)