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  "body": "\n## Summary\n\nA right Goldie ring is a [[ring|0B1261B5ED]] with two finiteness conditions.\nIt contains no infinite direct sum of nonzero right ideals, and it has the ascending chain condition on right [[annihilators|HB4XDKJTW8]].\nEvery right [[Noetherian ring|0670T59HGE]] is right Goldie, and so is every commutative integral domain.\nThese are the conditions in [[Goldie's theorem|MDS8655N0Z]], which describes the semiprime right Goldie rings as the rings with a semisimple Artinian [[classical ring of quotients|C5971PGKPH]].\n\n## Explanations\n\n### L1 human\n\nThe Goldie conditions are much weaker than the Noetherian condition, but they are strong enough to make the ring behave like a ring with finitely many \"directions\".\nThe first condition says that one cannot place infinitely many independent right ideals side by side.\nThe second condition limits only the special right ideals that arise as annihilators.\nFor example, an infinite product of copies of a field is not Goldie, because the copies of the field in each coordinate give infinitely many independent ideals.\n",
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  "name": "Goldie ring",
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