Geodesic
Holland’s theorem for pseudo-effect algebras
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 47-59

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We give two variations of the Holland representation theorem for $\ell $-groups and of its generalization of Glass for directed interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo $MV$-algebra can be represented as a pseudo-effect algebra or as a pseudo $MV$-algebra of automorphisms of some antilattice or of some linearly ordered set.
Classification : 03B50, 03G12, 06F20
Keywords: pseudo-effect algebra; pseudo $MV$-algebra; antilattice; prime ideal; automorphism; unital po-group; unital $\ell $-group 
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     title = {Holland{\textquoteright}s theorem for pseudo-effect algebras},
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     pages = {47--59},
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     volume = {56},
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     zbl = {1164.06329},
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Dvurečenskij, Anatolij. Holland’s theorem for pseudo-effect algebras. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 47-59. http://geodesic.mathdoc.fr/item/CMJ_2006__56_1_a4/