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A gg-Cancellative Semistar Operation on an Integral Domain Need Not Be gh-Cancellative

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Rings, Polynomials, and Modules

Abstract

Let D be an integral domain with quotient field K, let h (resp., g, f) be the non-zero D-submodules of K (resp., the non-zero fractional ideals of D, the finitely generated non-zero fractional ideals of D), and let {x, y} be a subset of the set {f, g, h} of symbols. For a semistar operation ⋆ on D, if (EE 1)⋆ = (EE 2)⋆ implies E 1 ⋆ = E 2 ⋆ for every E ∈ x and every E 1, E 2 ∈ y, then ⋆ is called xy-cancellative. We prove that a gg-cancellative semistar operation on an integral domain need not be gh-cancellative.

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References

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Authors and Affiliations

  1. Ibaraki University, Mito, Ibaraki, 310-0903, Japan

    Ryûki Matsuda

Authors
  1. Ryûki Matsuda
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Correspondence to Ryûki Matsuda .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Rome, Italy

    Marco Fontana

  2. Department of Analysis and Number Theory, Graz University of Technology, Graz, Austria

    Sophie Frisch

  3. Department of Mathematics, University of Connecticut, Storrs, Connecticut, USA

    Sarah Glaz

  4. Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Rome, Italy

    Francesca Tartarone

  5. Dipartimento di Matematica, Università di Padova, Padova, Italy

    Paolo Zanardo

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Matsuda, R. (2017). A gg-Cancellative Semistar Operation on an Integral Domain Need Not Be gh-Cancellative. In: Fontana, M., Frisch, S., Glaz, S., Tartarone, F., Zanardo, P. (eds) Rings, Polynomials, and Modules. Springer, Cham. https://doi.org/10.1007/978-3-319-65874-2_15

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