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On almost-divided domains

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Abstract

Let B be a domain, Q a maximal ideal of B, π: B → B/Q the canonical surjection, D a subring of B/Q, and A:=π −1(D). If both B and D are almost-divided domains (resp., n-divided domains), then A = B × B/Q D is an almost-divided domain (resp., an n-divided domain); the converse holds if B is quasilocal. If 2 ≤ d ≤ ∞, an example is given of an almost-divided domain of Krull dimension d which is not a divided domain.

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Authors and Affiliations

  1. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996-0612, USA

    David E. Dobbs

  2. Laboratoire de Mathématiques, Université Blaise Pascal, 63177, Aubière Cedex, France

    Gabriel Picavet

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  1. David E. Dobbs
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  2. Gabriel Picavet
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Correspondence to David E. Dobbs.

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Dobbs, D.E., Picavet, G. On almost-divided domains. Rend. Circ. Mat. Palermo 58, 199–210 (2009). https://doi.org/10.1007/s12215-009-0016-0

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  • DOI: https://doi.org/10.1007/s12215-009-0016-0

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