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The decomposition of linearly ordered pseudo-hoops

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Abstract

We generalize to the non-commutative case a construction of the Hájek decomposition using an equivalence relation on linear pseudo-hoops. Other two equivalence relations are used to obtain the Agliano–Montagna and the Cignoli–Esteva–Godo–Torrens decompositions. The comparability of the three decompositions follows from this construction.

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Notes

  1. The author’s participation at LATD 2012 was made possible by a travel grant and local support from the organizers.

References

  • Agliano P, Montagna F (2003) Varieties of BL-algebras I: general properties. J Pure Appl Algebra 181:105–129

    Article  MathSciNet  MATH  Google Scholar 

  • Busaniche M (2004) Decomposition of BL-chains. Algebra Universalis 52:519–525

    Article  MathSciNet  MATH  Google Scholar 

  • Ceterchi R (2001) Pseudo–Wajsberg algebras. Mult-Valued Log 6(1–2):67–88 (a special issue dedicated to the memory of Gr. C. Moisil)

    MathSciNet  MATH  Google Scholar 

  • Ceterchi R (2012) The Decomposition of linearly ordered pseudo-hoops. In: LATD 2012, 10–14 September 2012, Kanazawa, Ishikawa, Japan

  • Ceterchi R (2014) A categorical equivalence for a class of product pseudo-hoops. In: Proceedings of the workshop “Theory Day in Computer Science (DACS 2014)”, Analele Universitatii Bucuresti, Informatica, Anul LXI, pp 105–115

  • Cignoli R, Esteva F, Godo L, Torrens A (2000) Basic fuzzy logic is the logic of continuous t-norms and their residua. Soft Comput 4:106–112

    Article  Google Scholar 

  • Di Nola A, Georgescu G, Iorgulescu A (2002a) Pseudo-BL algebras I. Mult-Valued Log 8:673–714

  • Di Nola A, Georgescu G, Iorgulescu A (2002b) Pseudo-BL algebras II. Mult-Valued Log 8:715–750

  • Dvurecenskij A (2007a) Agliano–Montagna type decomposition of linear pseudo-hoops and its applications. J Pure Appl Algebra 211:851–861

  • Dvurecenskij A (2007b) Every linear pseudo-BL algebra admits a state. Soft Comput 11:495–501

  • Fuchs L (1963) Partially ordered algebraic systems. Pergamon Press, New York

    MATH  Google Scholar 

  • Georgescu G, Iorgulescu A (2001) Pseudo-MV algebras. Mult-Valued Log 6:95–135

    MathSciNet  MATH  Google Scholar 

  • Georgescu G, Leustean L, Preoteasa V (2005) Pseudo-hoops. J Mult-Valued Log Soft Comput 11:153–184

    MathSciNet  MATH  Google Scholar 

  • Hájek P (1998) Basic fuzzy logic and BL-algebras. Soft Comput 2:124–128

    Article  Google Scholar 

  • Laskowski MC, Shashoua YD (2002) A classification of BL-algebras. Fuzzy Sets Syst 131:271–282

    Article  MathSciNet  MATH  Google Scholar 

  • Mostert PS, Shields AL (1957) On the structure of semigroups on a compact manifold with boundary. Ann Math 65:117–143

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The author’s participation to LATD 2012 was possible due to a travel grant and to local support from the organizers.

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Authors and Affiliations

  1. Faculty of Mathematics and CS, University of Bucharest, 14 Academiei st., 010014, Bucharest, Romania

    Rodica Ceterchi

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  1. Rodica Ceterchi
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Correspondence to Rodica Ceterchi.

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The author declares that, apart from the above, she has no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by A. Di Nola.

An early version of this work was presented at LATD 2012, and has appeared in an extended abstract (Ceterchi 2012).

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Ceterchi, R. The decomposition of linearly ordered pseudo-hoops. Soft Comput 21, 5631–5639 (2017). https://doi.org/10.1007/s00500-016-2304-x

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  • DOI: https://doi.org/10.1007/s00500-016-2304-x

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