Skip to main content
SpringerLink
Log in

⊕-Cofinitely Supplemented Modules

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

Let R be a ring and M a right R-module. M is called ⊕-cofinitely supplemented if every submodule N of M with M/N finitely generated has a supplement that is a direct summand of M. In this paper various properties of the ⊕-cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of ⊕-cofinitely supplemented modules is ⊕-cofinitely supplemented. (2) A ring R is semiperfect if and only if every free R-module is ⊕-cofinitely supplemented. In addition, if M has the summand sum property, then M is ⊕-cofinitely supplemented iff every maximal submodule has a supplement that is a direct summand of M.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, Ondokuz Mayıs University, 05189, Amasya-Turkey, hcalisici@omu.edu.tr

    H. Çalişici

  2. Department of Mathematics, Faculty of Arts and Science, Ondokuz Mayıs University, 55139, Samsun-Turkey

    A. Pancar

Authors
  1. H. Çalişici
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Pancar
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Çalişici, H., Pancar, A. ⊕-Cofinitely Supplemented Modules. Czech Math J 54, 1083–1088 (2004). https://doi.org/10.1007/s10587-004-6453-1

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10587-004-6453-1

Keywords

Search

Navigation