Congruences and ideals in pseudo effect algebras as total algebras |
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Authors: | Silvia Pulmannová Elena Vinceková |
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Affiliation: | 1. Mathematical Institute, Slovak Academy of Sciences, ?tefánikova 49, 814 73, Bratislava, Slovakia
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Abstract: | Congruences and ideals in pseudo-effect algebras and their total algebra versions are studied. It is shown that every congruence of the total algebra induces a Riesz congruence in the corresponding pseudo-effect algebra. Conversely, to every normal Riesz ideal in a pseudo-effect algebra there is a total algebra, in which the given ideal induces a congruence of the total algebra. Ideals of total algebras corresponding to lattice-ordered pseudo-effect algebras are characterized, and it is shown that they coincide with normal Riesz ideals in the pseudo-effect algebras. |
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