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Kite Pseudo Effect Algebras

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Abstract

We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected with partially ordered groups not necessarily with strong unit. In such a case, starting even with an Abelian po-group, we can obtain a noncommutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz Decomposition Properties. Kites are so-called perfect pseudo effect algebras, and we define conditions when kite pseudo effect algebras have the least non-trivial normal ideal.

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Notes

  1. Notational convention: ⊙ binds stronger than ⊕.

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Acknowledgements

The author is very indebted to anonymous referees for their careful reading and suggestions which helped me to improve the readability of the paper.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 81473, Bratislava, Slovakia

    Anatolij Dvurečenskij

  2. Depart. Algebra Geom., Palacký University, 17. listopadu 12, 77146, Olomouc, Czech Republic

    Anatolij Dvurečenskij

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  1. Anatolij Dvurečenskij
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Correspondence to Anatolij Dvurečenskij.

Additional information

The paper has been supported by Slovak Research and Development Agency under the contract APVV-0178-11, the grant VEGA No. 2/0059/12 SAV, and by CZ.1.07/2.3.00/20.0051.

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Dvurečenskij, A. Kite Pseudo Effect Algebras. Found Phys 43, 1314–1338 (2013). https://doi.org/10.1007/s10701-013-9748-y

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