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  "body": "\n## Definition\n\nA field is a [[commutative ring|0GYGHKX834]] $K$ with these two properties.\n\n1. $1 \\neq 0$ in $K$.\n2. Every nonzero element of $K$ is a [[unit|019NFGFPR5]]: for each $a \\in K$ with $a \\neq 0$, there is $b \\in K$ with $a b = 1$.\n\n## Remarks\n\nThe rings $\\mathbb{Q}$, $\\mathbb{R}$ and $\\mathbb{C}$ are fields. The ring $\\mathbb{Z}$ is not a field.\nFor a prime number $p$, the ring [[$\\mathbb{Z}/p\\mathbb{Z}$ is a field|0NV6E43P4A]].\nEvery field is an [[integral domain|09S3PFBEPM]].\nA [[division ring|0WZXK05ME7]] has the same axioms without the commutativity of the multiplication.\n\n## Explanations\n\n### L1 human\n\nA field is a number system where the four operations of arithmetic work.\nYou can add, subtract, multiply, and divide by any number that is not zero.\nThe rational numbers are the simplest example.\n",
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