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The exocenter and type decomposition of a generalized pseudoeffect algebra

David J. FoulisSilvia PulmannováElena Vinceková — 2013

Discussiones Mathematicae - General Algebra and Applications

We extend the notion of the exocenter of a generalized effect algebra (GEA) to a generalized pseudoeffect algebra (GPEA) and show that elements of the exocenter are in one-to-one correspondence with direct decompositions of the GPEA; thus the exocenter is a generalization of the center of a pseudoeffect algebra (PEA). The exocenter forms a boolean algebra and the central elements of the GPEA correspond to elements of a sublattice of the exocenter which forms a generalized boolean algebra. We extend...

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