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THE LOOMIS–SIKORSKI THEOREM FOR
$EMV$-ALGEBRAS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 106 / Issue 2 / April 2019
- Published online by Cambridge University Press:
- 23 August 2018, pp. 200-234
- Print publication:
- April 2019
-
- Article
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- You have access
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An EMV-algebra resembles an MV-algebra in which a top element is not guaranteed. For
$\unicode[STIX]{x1D70E}$-complete 
$EMV$-algebras, we prove an analogue of the Loomis–Sikorski theorem showing that every 
$\unicode[STIX]{x1D70E}$-complete 
$EMV$-algebra is a 
$\unicode[STIX]{x1D70E}$-homomorphic image of an 
$EMV$-tribe of fuzzy sets where all algebraic operations are defined by points. To prove it, some topological properties of the state-morphism space and the space of maximal ideals are established.
