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 unique eludes us; yet we remain faithful to the ideal of it; and in spite of sense and of our merely abstract thinking, it becomes for us the most real thing in the actual world, although for us it is the elusive goal of an infinite quest.”
—Josiah Royce (1855–1916)
“The vice named surrealism is the immoderate and impassioned use of the stupefacient image or rather of the uncontrolled provocation of the image for its own sake and for the element of unpredictable perturbation and of metamorphosis which it introduces into the domain of representation; for each image on each occasion forces you to revise the entire Universe.”
—Louis Aragon (1897–1982)