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  "body": "\n## Summary\n\nA presentation of an algebra in a [[variety|AJNZJD8442]] describes it by generators and relations.\nThe relations are equations between terms in the generators.\nThe presented algebra is the quotient of the free algebra on the generators by the smallest congruence that makes the relations true.\nEvery algebra of the variety has a presentation, and finitely presented algebras are those with finitely many generators and relations.\n[[Presentations of groups|0JGEQXQ4AC]] are the case of the variety of groups.\n\n## Explanations\n\n### L1 human\n\nTo describe an algebra, name some elements that generate it and list the equations they satisfy.\nThe algebra is then the \"most general\" one in which these equations hold, and nothing more.\nFor example, in commutative rings with identity, one generator $x$ and the relation $x^2 = -1$ present the Gaussian integers $\\Z[i]$.\nIn monoids, generators $a, b$ with relation $ab = ba$ present the monoid $\\N^2$ under addition.\n",
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