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  "body": "\n## Summary\n\nA finite ring is a [[ring|0B1261B5ED]] with only finitely many elements.\nThe rings $\\Z/n\\Z$ of [[integers modulo n|03VFZ2WETT]], the [[finite fields|0ZXZ82FTX2]] and the matrix rings over them are the basic examples.\nFiniteness forces strong structure: by [[Wedderburn's little theorem|0RRNVX1VKA]], every finite division ring is a field.\nFinite rings are used in number theory, combinatorics and coding theory.\n\n## Explanations\n\n### L1 human\n\nA finite ring is a number system with only finitely many numbers, where you can add, subtract and multiply.\nClock arithmetic is the main picture: on a clock with $12$ hours, $9 + 5 = 2$ and $3 \\cdot 4 = 0$.\nThis gives the ring $\\Z/12\\Z$ with $12$ elements.\nIn a finite ring, repeated addition of $1$ must come back to $0$, so the ring always has a positive characteristic.\n",
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