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Ideally

two-sided ideal

noun

(algebra) A subring which is both a left ideal and a right ideal. Commonly referred to simply as an ideal, but referred to as two-sided ideal for emphasis.

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principal ideal ring

noun

(algebra, ring theory) A commutative ring in which every ideal is a principal ideal.

A principal ideal ring is a ring in which every ideal is principal.

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principal ideal rings

noun

plural of principal ideal ring

Principal ideal rings are an important concept in abstract algebra.

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principal ideal domains

noun

plural of principal ideal domain

Principal ideal domains are integral domains in which every ideal is principal.

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two-sided ideals

noun

plural of two-sided ideal

Two-sided ideals are important in ring theory.

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