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  "body": "\n## Summary\n\nThe subalgebra generated by a subset $X$ of an [[algebra|QJGPT2W0FT]] is the smallest [[subalgebra|676H7EGTKJ]] that contains $X$.\nIts elements are the values of all terms in the operations applied to elements of $X$ and to the constants.\nThe [[subgroup generated by a subset|0RP7VWQ0YN]] and the [[ideal generated by a subset|0GSW76Q14N]] are special cases of this idea.\nThe map that sends $X$ to the subalgebra it generates is a [[closure operator|2HJGRABSPZ]], and an algebra generated by a finite set is [[finitely generated|WR4WF1K2KW]].\n\n## Explanations\n\n### L1 human\n\nStart with some elements, then apply the operations to them again and again, and collect everything you get.\nThe result is the generated subalgebra: it contains the starting elements and is closed under the operations, and nothing smaller has both properties.\nIn the integers with addition, negation and $0$, starting from $4$ and $6$ you get $10$, $2 = 6 - 4$, and then all multiples of $2$.\nSo $\\set{4, 6}$ generates the even integers.\n",
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