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  "body": "\n## Summary\n\nA relatively free algebra is an algebra that is free over some of its generating sets in the variety that it generates.\nThe word \"relatively\" contrasts it with absolutely free algebras: it is free relative to the identities that it satisfies.\nFree groups, free abelian groups, free nilpotent groups of a given class and polynomial rings are relatively free.\nRelatively free algebras are exactly the free algebras of all varieties.\n\n## Explanations\n\n### L1 human\n\nAn algebra is relatively free when some generators can be sent anywhere inside the algebra itself and the map always extends to an endomorphism.\nFor example, in $\\Z^2$ the generators $(1, 0)$ and $(0, 1)$ can be sent to any two vectors, and a $2 \\times 2$ integer matrix does the rest.\nSo $\\Z^2$ is relatively free: it is the free algebra on two generators of the variety of abelian groups.\n",
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