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

Ryûki Matsuda ()
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Ryûki Matsuda: Ibaraki University

A chapter in Rings, Polynomials, and Modules, 2017, pp 299-305 from Springer

Abstract: 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.

Keywords: Star operation; Semistar operation; 13A15 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-65874-2_15

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DOI: 10.1007/978-3-319-65874-2_15

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