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Direct product decompositions of bounded commutative residuated ℓ-monoids

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Abstract

The notion of bounded commutative residuated ℓ-monoid (BCR ℓ-monoid, in short) generalizes both the notions of MV-algebra and of BL-algebra. Let

be a BCR ℓ-monoid; we denote by ℓ(

) the underlying lattice of

. In the present paper we show that each direct product decomposition of ℓ(

) determines a direct product decomposition of

. This yields that any two direct product decompositions of

have isomorphic refinements. We consider also the relations between direct product decompositions of

and states on

.

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Authors and Affiliations

  1. Matematický ústav SAV, Grešákova 6, 040 01, Košice, Slovakia

    Ján Jakubík

Authors
  1. Ján Jakubík
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Correspondence to Ján Jakubík.

Additional information

This work was supported by Slovak Research and Development Agency under the contract No APVV-0071-06.

This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information (grant I/2/2005).

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Jakubík, J. Direct product decompositions of bounded commutative residuated ℓ-monoids. Czech Math J 58, 1129–1143 (2008). https://doi.org/10.1007/s10587-008-0074-z

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  • DOI: https://doi.org/10.1007/s10587-008-0074-z

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