Abstract
Recently a new family of pseudo effect algebras, called kite pseudo effect algebras, was introduced. Such an algebra starts with a po-group G, a set I and with two bijections λ,ρ:I→I. Using a clever construction on the ordinal sum of (G +)I and (G −)I, we can define a pseudo effect algebra which can be non-commutative even if G is an Abelian po-group. In the paper we give a characterization of subdirect product of subdirectly irreducible kite pseudo effect algebras, and we show that every kite pseudo effect algebra is an interval in a unital po-loop.
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The authors are very indebted to an anonymous referee for his/her careful reading and suggestions which helped to improve the readability of the paper.
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This work was supported by the Slovak Research and Development Agency under contract APVV-0178-11, grant VEGA No. 2/0059/12 SAV, and CZ.1.07/2.3.00/20.0051.
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Dvurečenskij, A., Holland, W.C. Some Remarks on Kite Pseudo Effect Algebras. Int J Theor Phys 53, 1685–1696 (2014). https://doi.org/10.1007/s10773-013-1966-8
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DOI: https://doi.org/10.1007/s10773-013-1966-8