Recent zbMATH articles in MSC 20A
https://www.zbmath.org/atom/cc/20A
2021-02-27T13:50:00+00:00
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A representation theorem for measurable relation algebras.
https://www.zbmath.org/1453.03071
2021-02-27T13:50:00+00:00
"Givant, Steven"
https://www.zbmath.org/authors/?q=ai:givant.steven-r
"AndrĂ©ka, Hajnal"
https://www.zbmath.org/authors/?q=ai:andreka.hajnal
Summary: A relation algebra is called measurable when its identity is the sum of measurable atoms, where an atom is called measurable if its square is the sum of functional elements.
In this paper we show that atomic measurable relation algebras have rather strong structural properties: they are constructed from systems of groups, coordinated systems of isomorphisms between quotients of the groups, and systems of cosets that are used to ``shift'' the operation of relative multiplication. An atomic and complete measurable relation algebra is completely representable if and only if there is a stronger coordination between these isomorphisms induced by a scaffold (the shifting cosets are not needed in this case). We also prove that a measurable relation algebra in which the associated groups are all finite is atomic.