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  "body": "\n## Definition\n\nLet $(M, \\cdot)$ be a [[magma|9689SFPVE9]].\nIt is a *commutative magma* if $x \\cdot y = y \\cdot x$ for all $x, y \\in M$, that is, if the operation has the [[commutativity|099E72KTF8]] property.\n\n## Remarks\n\nExample: $\\Q$ with $x \\circ y = (x + y)/2$.\nThe value is rational, and $(x + y)/2 = (y + x)/2$.\nThe magma is not associative: $(0 \\circ 4) \\circ 8 = 5$ but $0 \\circ (4 \\circ 8) = 3$.\n\nNon-example: $(\\Z, -)$, since $1 - 0 = 1$ but $0 - 1 = -1$.\n\nIn Mathlib this structure is the class `CommMagma`.\n",
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