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The study of algebraic structures and properties applying to large classes of such structures. For example, ideas from group theory and ring theory are extended and considered for structures with other signatures (systems of basic or fundamental operations).
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Representation of free Boolean sigma-algebras
There appears to be some confusion in the question, which I will try to dispel.
As a free Boolean $\sigma$-algebra $A$ is a Boolean $\sigma$-algebra, the Loomis-Sikorski theorem certainly applies. Ho …