Original Paper

Weakly minimal modules over integral group rings and over related classes of rings

  1. Stefano Leonesi,
  2. Sonia L'Innocente,
  3. Carlo Toffalori

Article first published online: 28 SEP 2005

DOI: 10.1002/malq.200410053

Issue

Mathematical Logic Quarterly

Mathematical Logic Quarterly

Volume 51, Issue 6, pages 613–625, November 2005

Additional Information

How to Cite

Leonesi, S., L'Innocente, S. and Toffalori, C. (2005), Weakly minimal modules over integral group rings and over related classes of rings. Mathematical Logic Quarterly, 51: 613–625. doi: 10.1002/malq.200410053

Author Information

  1. Dipartimento di Matematica e Informatica, Università di Camerino, Via Madonna delle Carceri 9, 62032 Camerino, Italy

Publication History

  1. Issue published online: 28 SEP 2005
  2. Article first published online: 28 SEP 2005
  3. Manuscript Accepted: 23 AUG 2005
  4. Manuscript Revised: 18 JUL 2005
  5. Manuscript Received: 28 OCT 2004

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Keywords:

  • Weakly minimal module;
  • Prüfer domain;
  • group ring;
  • Dedekind-like ring

Abstract

A module is weakly minimal if and only if every pp-definable subgroup is either finite or of finite index. We study weakly minimal modules over several classes of rings, including valuation domains, Prüfer domains and integral group rings. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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