ideal

Additive subgroup of a ring closed under multiplcation by arbitrary ring element

EntityQ44649

Subclass of: abelian group
, rng
, submodule
Part of: ring

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any integer results in an even number; these closure and absorption properties are the defining properties of an ideal. An ideal can be used to construct a quotient ring in a way similar to how, in group theory, a normal subgroup can be used to construct a quotient group.

Overview

All data

29 statements · 14% with external sources · numbers in brackets are citations

Studied by: ring theory
Different from: ideal
fractional ideal

On other databases

23 identifiers linking ideal across the web's reference databases

Data quality

statements

14%

externally sourced

Source last edited September 28, 2026. AIDB refreshes this page daily.

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AIDB. (2026). ideal (Q44649). Retrieved from https://aidb.si/e/ideal-Q44649