Unitizations of Generalized Pseudo Effect Algebras and their Ideals |
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Authors: | David J Foulis Sylvia Pulmannová Elena Vinceková |
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Institution: | 1.Department of Mathematics and Statistics,University of Massachusetts,Amherst,USA;2.Mathematical Institute,Slovak Academy of Sciences,Bratislava,Slovakia |
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Abstract: | A generalized pseudo effect algebra (GPEA) is a partially ordered partial algebraic structure with a smallest element 0, but not necessarily with a unit (i.e, a largest element). If a GPEA admits a so-called unitizing automorphism, then it can be embedded as an order ideal in its so-called unitization, which does have a unit. We study unitizations of GPEAs with respect to a unitizing automorphism, paying special attention to the behavior of congruences, ideals, and the Riesz decomposition property in this setting. |
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