# Definition:Ideal of Ring/Also known as

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## 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