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Modular \(\hbox {d}_{0}\)-algebras

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Abstract

We introduce a concept of modularity for a \(\hbox {d}_{0}\)-algebraA in such a way that, in case of A being a lattice, it coincides with the usual one. We also show that if \(\mu \) is a \(\hbox {d}_{0}\)-measure on a \(\hbox {d}_{0}\)-algebraA, the quotient of A modulo the ideal of \(\mu \)-negligible elements is always modular.

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Authors and Affiliations

  1. Dipartimento di Matematica, Informatica ed Economia, Università della Basilicata, viale dell’Ateneo Lucano, 10, 85100, Potenza, Italy

    Anna Avallone

  2. Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano (SA), Italy

    Giuseppina Barbieri

  3. Dipartimento di Matematica, Informatica ed Economia, Università della Basilicata, viale dell’Ateneo Lucano, 10, 85100, Potenza, Italy

    Paolo Vitolo

  4. Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, Via delle Scienze, 206, 33100, Udine, Italy

    Hans Weber

Authors
  1. Anna Avallone
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  2. Giuseppina Barbieri
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  3. Paolo Vitolo
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  4. Hans Weber
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Correspondence to Hans Weber.

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Avallone, A., Barbieri, G., Vitolo, P. et al. Modular \(\hbox {d}_{0}\)-algebras. Boll Unione Mat Ital 13, 529–538 (2020). https://doi.org/10.1007/s40574-020-00237-6

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