Abstract
We investigate the recently introduced two-sorted variety of equational states. We show that, similarly to MV-algebras, in equational states ideals are in bijection with two-sorted congruences. Differently from MV-algebras, not every equational state is the subdirect product of linearly ordered ones. We finally show that the variety of equational states is not generated by the linearly ordered ones.
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Acknowledgement
The authors are indebted with Prof. Vincenzo Marra for suggesting the Example 2. This work was supported by the PRIN2017 “Theory and applications of resource sensitive logics”. S. Lapenta was also funded by the POC Innovazione e Ricerca 2014-2020, project AIM1834448-1 and the Research Grant “Un approccio algebrico alla statistica per applicazioni industriali”.
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Lapenta, S., Napolitano, S., Spada, L. (2023). Ideals in the Two-Sorted Variety of Equational States. In: Massanet, S., Montes, S., Ruiz-Aguilera, D., González-Hidalgo, M. (eds) Fuzzy Logic and Technology, and Aggregation Operators. EUSFLAT AGOP 2023 2023. Lecture Notes in Computer Science, vol 14069. Springer, Cham. https://doi.org/10.1007/978-3-031-39965-7_41
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DOI: https://doi.org/10.1007/978-3-031-39965-7_41
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