principal ideal

Noun

Meaning

principal ideal (plural principal ideals)

(algebra) An ideal I in an algebraic object R (which could be a ring, algebra, semigroup or lattice) that is generated by a given single element a ∈ R; the smallest ideal that contains a.

Synonyms

Examples

All Euclidean domains and all fields are principal ideal domains. Source: Internet

Among the integers, the ideals correspond one-for-one with the non-negative integers : in this ring, every ideal is a principal ideal consisting of the multiples of a single non-negative number. Source: Internet

All Euclidean domains are principal ideal domains, but the converse is not true. Source: Internet

A valuation ring is not Noetherian unless it is a principal ideal domain. 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

A principal ideal domain is an integral domain in which every ideal is principal. Source: Internet

Close letter words and terms