principal ideal

noun

, Mathematics.

1. 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.

Word History and Origins

Origin of principal ideal¹

First recorded in 1935–40

Example Sentences

The symphonic poem in the form in which Liszt has given it to us, is ordinarily an ensemble of different movements depending on each other, and flowing from a principal ideal, blending into each other, and forming one composition.

From Project Gutenberg

He is guided by ideals; but his principal ideal takes the form of an acceptance of the world as it is, independently of his ideals.

From Project Gutenberg

The principal ideal of the Church is saintliness.

From Project Gutenberg

Europe has been eclipsed because her Church—her soul—has been eclipsed; the Church has been eclipsed because her principal ideal has been eclipsed.

From Project Gutenberg