Definition:Ideal of Ring/Also known as

Ideal of Ring: Also known as

An ideal can also be referred to as a two-sided ideal to distinguish it from a left ideal and a right ideal.

Some sources use $I$ to denote an ideal, but on $\mathsf{Pr} \infty \mathsf{fWiki}$ this can be too easily conflated with an identity mapping.

Some sources refer to such a two-sided ideal as a normal subring, in apposition with the concept of a normal subgroup.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): normal subring
• 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Algebraic Concepts
• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 6$: Rings and fields
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): ideal
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): ideal

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• 2007: Svetlana Katok: p-adic Analysis Compared with Real ... (previous) ... (next): $\S 1.8$ Algebraic properties of $p$-adic integers