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Keywords:
pseudo-effect algebra; pseudo $MV$-algebra; antilattice; prime ideal; automorphism; unital po-group; unital $\ell $-group
pseudo-effect algebra; pseudo $MV$-algebra; antilattice; prime ideal; automorphism; unital po-group; unital $\ell $-group
Summary:
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.
References:
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