Euclidean domain

Noun

Meaning

Euclidean domain (plural Euclidean domains)

(algebra) an integral domain in which division with remainder is possible

Source: en.wiktionary.org

Examples

A Euclidean domain is an integral domain which can be endowed with at least one Euclidean function. Source: Internet

A field norm is a Dedekind-Hasse norm; thus, (5) shows that a Euclidean domain is a PID. Source: Internet

As a Euclidean domain It is easy to see graphically that every complex number is within units of a Gaussian integer. Source: Internet

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

An example of a principal ideal domain that is not a Euclidean domain is the ring Wilson, Jack C. "A Principal Ring that is Not a Euclidean Ring." Source: Internet

However, if there is no "obvious" Euclidean function, then determining whether R is a PID is generally a much easier problem than determining whether it is a Euclidean domain. Source: Internet

Close letter words and terms

Euclidean axiom Euclidean distance Euclidean division Euclidean geometry Euclidean group Euclidean metric