principal ideal

English

Noun

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

(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

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