/ Dictionary / Index P principal ideal domain: Meaning and Definition of Find definitions for: prin'cipal ide'al domain' Pronunciation: [key] — Math. Math. a commutative integral domain with multiplicative identity in which every ideal is principal. Also called Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease. principal ideal principality 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