Abstract
As is well-known, every generalized effect algebra can be embedded as a maximal proper ideal in an effect algebra called its unitization. We show that a necessary and sufficient condition that a generalized pseudo effect algebra can similarly be embedded as a maximal proper ideal in a pseudo effect algebra is that it admits a so-called unitizing automorphism. On the other hand, we show that a pseudo effect algebra is a unitization of a generalized pseudo effect algebra if and only if it admits a two-valued state.
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