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  "body": "\n## Summary\n\nThe dimension of a [[central simple algebra|5HRKJBAY2V]] over its center is always a perfect square $n^2$.\nThe number $n$ is the degree of the algebra.\nIt is the size of the matrices that the algebra becomes over an algebraically closed field.\nIt bounds the index and the period of the algebra.\n\n## Explanations\n\n### L1 human\n\nThe algebra of $n \\times n$ matrices over a field has dimension $n^2$, and its degree is $n$.\nEvery central simple algebra becomes such a matrix algebra over a large enough field, so its dimension is also a square.\nHamilton's quaternions have dimension $4$ over $\\R$, so their degree is $2$; over $\\C$ they become the $2 \\times 2$ complex matrices.\n",
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