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Subdirectly irreducible state-morphism BL-algebras

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Abstract

Recently Flaminio and Montagna (Proceedings of the 5th EUSFLAT Conference, II: 201–206. Ostrava, 2007), (Inter. J. Approx. Reason. 50:138–152, 2009) introduced the notion of a state MV-algebra as an MV-algebra with internal state. We have two kinds: state MV-algebras and state-morphism MV-algebras. These notions were also extended for state BL-algebras in (Soft Comput. doi:10.1007/s00500-010-0571-5). In this paper, we completely describe subdirectly irreducible state-morphism BL-algebras and this generalizes an analogous result for state-morphism MV-algebras presented in (Ann. Pure Appl. Logic 161:161–173, 2009).

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

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  1. Anatolij Dvurečenskij
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Correspondence to Anatolij Dvurečenskij.

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The author thanks for the support by Center of Excellence SAS—Quantum Technologies—, ERDF OP R&D Projects CE QUTE ITMS 26240120009, the grant VEGA No. 2/0032/09 SAV and by the Slovak Research and Development Agency under the contract No. APVV-0071-06, Bratislava.

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Dvurečenskij, A. Subdirectly irreducible state-morphism BL-algebras. Arch. Math. Logic 50, 145–160 (2011). https://doi.org/10.1007/s00153-010-0206-7

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  • DOI: https://doi.org/10.1007/s00153-010-0206-7

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