English

The Loomis--Sikorski Theorem for $EMV$-algebras

Commutative Algebra 2017-07-04 v1

Abstract

Recently, in [DvZa], we have introduced EMVEMV-algebras which resemble MVMV-algebras but the top element is not guaranteed for them. For σ\sigma-complete EMVEMV-algebras, we prove an analogue of the Loomis--Sikorski Theorem showing that every σ\sigma-complete EMVEMV-algebra is a σ\sigma-homomorphic image of an EMVEMV-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}
}