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  "body": "\n## Summary\n\nA partial algebra is a set with operations that need not be defined for every choice of arguments.\nIt generalises the [[algebraic structure|QJGPT2W0FT]] of universal algebra, where every operation is total.\nPartial algebras model structures such as fields, where the inverse of $0$ is not defined, and categories, where two arrows compose only when they match.\n\n## Explanations\n\n### L1 human\n\nIn an ordinary algebra you can combine any elements and always get an answer.\nIn a partial algebra some combinations are simply not allowed.\nA field is the classic example: you can divide by any element except $0$.\nAnother example is the set of natural numbers with subtraction, where $3 - 5$ has no value in $\\N$.\nThe theory of partial algebras asks which tools of universal algebra still work when operations have gaps.\n",
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