The Loomis--Sikorski Theorem for $EMV$-algebras
Commutative Algebra
2017-07-04 v1
Abstract
Recently, in [DvZa], we have introduced -algebras which resemble -algebras but the top element is not guaranteed for them. For -complete -algebras, we prove an analogue of the Loomis--Sikorski Theorem showing that every -complete -algebra is a -homomorphic image of an -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.
Keywords
Cite
@article{arxiv.1707.00270,
title = {The Loomis--Sikorski Theorem for $EMV$-algebras},
author = {Anatolij Dvurečenskij and Omid Zahiri},
journal= {arXiv preprint arXiv:1707.00270},
year = {2017}
}