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Somewhere (in some book) I have read and added to my notes following definition:

Given a set $X$ a semi-algebra is a subset $\mathcal{S}\subseteq \mathcal{P}(X)$ such that

  1. $X\in\mathcal{S}$;
  2. for all $A,B\in\mathcal{S}$, then $A\cap B\in\mathcal{S}$; and
  3. for all $A\in\mathcal{S}$, then there are finitely many $A_k\in\mathcal{S}$ such that $A^C=\bigcup_{k=1}^n A_k$ with disjoint union.

I can't find anything about it using search engines, thus the defined object must have some other, more official, name. Any idea?

Mohamed Ali
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    semi-algebra is a pretty common name and was asked here often before, e.g. check:

    https://math.stackexchange.com/questions/256606/question-about-definition-of-semi-algebra https://math.stackexchange.com/questions/1135203/question-about-the-definition-of-a-semialgebra

    or german wikipedia: https://de.wikipedia.org/wiki/Semialgebra (unfortunately I couldn't find an english entry)

     – Gono Dec 08 '19 at 12:25
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    See Semi-ring of sets. – Mauro ALLEGRANZA Dec 08 '19 at 13:13
  • @AaronLenz My comment was automatically generated by MSE. Gono provided the link, and you seemed to assert that the link answered your question. As such, I flagged this question as a duplicate, at which point the comment was automatically generated. – Xander Henderson Dec 08 '19 at 23:24

1 Answers1

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On Wikipedia it's called a semiring of sets also in my measure theory texts, though the Germans seem to prefer Semialgebra, which why your surname (Lenz) might be the reason you come at it from this name.

Henno Brandsma
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