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Congruences and ideals in pseudo effect algebras as total algebras

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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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Acknowledgments

This work was supported by the Slovak Research and Development Agency under the contract No. LPP-0199-07 and APVV-0071-06; by the Slovak-Italian project SK-IT 0016-08, ERDF OP R&D Project CE QUTE ITMS 26240120009 and grant VEGA 2/0032/09.

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  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Silvia Pulmannová & Elena Vinceková

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  1. Silvia Pulmannová
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  2. Elena Vinceková
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Correspondence to Elena Vinceková.

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Pulmannová, S., Vinceková, E. Congruences and ideals in pseudo effect algebras as total algebras. Soft Comput 14, 1209–1215 (2010). https://doi.org/10.1007/s00500-009-0532-z

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