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  "body": "\n## Summary\n\nA generalized Boolean algebra is a [[distributive lattice|0HM0HQCK6N]] with a least element $0$ in which any two elements $a$ and $b$ have a difference $a \\setminus b$.\nThis difference is the complement of $a \\wedge b$ in the interval $[0, a]$.\nIt is a [[Boolean algebra|0XADJKM699]] that may lack a greatest element.\nEach interval $[0, a]$ in it is a Boolean algebra.\nGeneralized Boolean algebras correspond to Boolean rings that need not have a unit, in the same way as Boolean algebras correspond to [[Boolean rings|0RCV1ZFP8G]].\n\n## Explanations\n\n### L1 human\n\nThink of the finite subsets of the natural numbers.\nYou can take unions, intersections and differences of two finite sets and stay finite.\nYou cannot take the complement of a finite set, because it is infinite.\nSo the finite sets have set difference but no global complement.\nA generalized Boolean algebra is exactly this kind of structure: Boolean algebra with differences, but with no top element required.\n",
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