/ Dictionary / Index P principal ideal: Meaning and Definition of Find definitions for: prin'cipal ide'al Pronunciation: [key] — Math. Math. the smallest ideal containing a given element in a ring; an ideal in a ring with a multiplicative identity, obtained by multiplying each element of the ring by one specified element. Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease. principal focus principal ideal domain Related Content Daily Word Quiz: mamba Analogy of the Day: Today’s Analogy Spelling Bee: Today’s Spelling Bee Frequently Misspelled Words Frequently Mispronounced Words Easily Confused Words Writing & Language