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  "body": "\n## Summary\n\nA rng, also called a non-unital ring, is a structure with all the axioms of a [[ring|0B1261B5ED]] except the existence of a multiplicative identity.\nThe name is \"ring\" without the letter \"i\", for \"identity\".\nRngs arise naturally: ideals, rings of functions with compact support, and many algebras in analysis have no unit element.\nEvery rng embeds as an ideal in a ring with identity, so much of ring theory still applies.\n\n## Explanations\n\n### L1 human\n\nA rng has addition and multiplication with the usual rules, but there may be no number $1$ that leaves every element unchanged.\nThe even integers $2\\Z$ are the standard example: they are closed under addition and multiplication, but $1$ is not even.\nNo even integer $e$ satisfies $e \\cdot 2 = 2$, so $2\\Z$ has no identity.\n",
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