Hostname: page-component-5c6d5d7d68-lvtdw Total loading time: 0 Render date: 2024-08-15T09:38:53.795Z Has data issue: false hasContentIssue false
  • English
  • Français

Stacked submodules of torsion modules over discrete valuation domains

Published online by Cambridge University Press:  17 April 2009

Pudji Astuti  and
Harald K. Wimmer
Pudji Astuti
Affiliation:
Departemen Matematika, Institut Teknologi Bandung, Bandung 40132, Indonesia, e-mail: pudji@dns.math.itb.ac.id
Harald K. Wimmer
Affiliation:
Mathematisches Institut, Universität Würzburg, D-97074 Würzburg, Germany, e-mail: wimmer@mathematik.uni-wuerzburg.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A submodule W of a torsion module M over a discrete valuation domain is called stacked in M if there exists a basis ℬ of M such that multiples of elements of ℬ form a basis of W. We characterise those submodules which are stacked in a pure submodule of M.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 439 - 447
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Adkins, W.A. and Weintraub, St.H., Algebra: An approach via module theory, Graduate Texts in Mathematics 136 (Springer-Verlag, New York, 1992).CrossRefGoogle Scholar
[2]Baer, R., ‘Types of elements and the characteristic subgroups of abelian groups’, Proc. London Math. Soc. 39 (1935), 481–514.CrossRefGoogle Scholar
[3]Bru, R., Rodman, L. and Schneider, H., ‘Extensions of Jordan bases for invariant subspaces of a matrix’, Linear Algebra Appl. 150 (1991), 209–225.CrossRefGoogle Scholar
[4]Cohen, J.M. and Gluck, H., ‘Stacked bases for modules over principal ideal domains’, J. Algebra 14 (1970), 493–505.CrossRefGoogle Scholar
[5]Fuchs, L., ‘Notes on Abelian groups, II’, Acta Math. Hungar. 11 (1960), 117–125.CrossRefGoogle Scholar
[6]Fuchs, L., Infinite Abelian groups, Vol. I, Pure and Applied Mathematics 36 (Academic Press, New York, 1973).Google Scholar
[7]Kaplanski, I., Infinite Abelian groups (University of Michigan Press, Ann Arbor, MI, 1954).Google Scholar