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State-morphism pseudo-effect algebras

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Abstract

The notion of a state-morphism on pseudo-effect algebras is introduced, and pseudo-effect algebras with distinguished state-morphisms are studied under the name state-morphism pseudo-effect algebras (SMPEAs). It is shown that every SMPEA admits a representation as a (total) state-morphism algebra, and some results from the general theory of state-morphism algebras (that is, algebras endowed with a distinguished idempotent endomorphism called a state-morphism), recently developed by Botur and Dvurečenskij, can be applied. In particular, it is shown that under suitable conditions, a SMPEA can be embedded into a so-called diagonal one, realized by a direct product of the SMPEA with itself endowed with a suitable natural state-morphism.

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Acknowledgments

This work was supported by ERDF OP R & D metaQUTE ITMS 26240120022, Grant VEGA 2/0059/12 and by Science and Technology Assistance Agency under the contract no. APVV-0178-11.

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Authors and Affiliations

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

    S. Pulmannová & E. Vinceková

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  1. S. Pulmannová
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  2. E. Vinceková
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Correspondence to E. Vinceková.

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Communicated by L. Spada.

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Pulmannová, S., Vinceková, E. State-morphism pseudo-effect algebras. Soft Comput 18, 5–13 (2014). https://doi.org/10.1007/s00500-013-1053-3

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