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principal ideal

American  

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.

Etymology

Origin of principal ideal

First recorded in 1935–40

Example Sentences

Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.

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 International Congress of Arts and Science, Volume I Philosophy and Metaphysics by Various

The principal ideal of the Church is saintliness.

From The Agony of the Church (1917) by Velimirović, Nikolai

Definitions and idiom definitions from Dictionary.com Unabridged, based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

Idioms from The American Heritage® Idioms Dictionary copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.