principal ideal

noun

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.

Similar
two-sided principal ideal
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Meanings

nounprincipal ideal (plural principal ideals)

plural principal ideals

  1. algebraAn 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: two-sided principal ideal

Synonyms & antonyms

nounAn 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.

Similar
two-sided principal ideal
Cite this entry
APA

principal ideal. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/principal%20ideal

MLA

“principal ideal.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/principal%20ideal. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “principal ideal,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/principal%20ideal.

Source: principal ideal on Wiktionary, CC BY-SA 4.0.