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  "body": "\n## Summary\n\nAn algebraic structure, or algebra, is a set together with a family of [[finitary operations|EJ8YJVM9BW]] on it.\nThe names and arities of the operations form a [[signature|WDVVEYD6AT]] with no relation symbols, so an algebraic structure is a [[structure|983GZBQYT4]] of a special kind.\nGroups, rings, fields, lattices and vector spaces are the main examples.\nA kind of algebraic structure is usually fixed by its signature and by a list of axioms, often identities, that the operations satisfy.\n\n## Explanations\n\n### L1 human\n\nAn algebraic structure is a set with ways to combine its elements.\nThe integers with addition, negation and the number $0$ form one: $+$ combines two integers, negation changes one integer, and $0$ is a fixed element.\nThe axioms say how these operations behave, for example $a + 0 = a$.\nA [[group|G5S1M9]] is an algebraic structure with one binary operation, one unary operation and one constant that satisfy the group axioms.\n",
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