principal ideal

English

Noun

principal ideal (plural principal ideals)

1. (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

• (smallest ideal that contains a given element): two-sided principal ideal

Derived terms

• left principal ideal
• principal fractional ideal
• principal ideal domain
• right principal ideal

Further reading

• Principal Ideal on Wolfram MathWorld
• Principal ideal on Encyclopedia of Mathemaics
• Ascending chain condition on principal ideals on Wikipedia.Wikipedia