Subdirectly irreducible state-morphism BL-algebras

Archive for Mathematical Logic 50 (1-2):145-160 (2011)

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)
Keywords State BL-algebra  State-morphism BL-algebra  BL-algebra  State-operator  State-morphism-operator  Subdirectly irreducible algebras
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DOI 10.1007/s00153-010-0206-7
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References found in this work BETA

Boolean Deductive Systems of BL-Algebras.Esko Turunen - 2001 - Archive for Mathematical Logic 40 (6):467-473.
States on Pseudo MV-Algebras.Anatolij Dvurečenskij - 2001 - Studia Logica 68 (3):301-327.
State-Morphism MV-Algebras.Antonio Di Nola & Anatolij Dvurečenskij - 2009 - Annals of Pure and Applied Logic 161 (2):161-173.

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