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Cofinitely semiperfect modules

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Abstract

It is well known that a projective module M is ⊕-supplemented if and only if M is semiperfect. We show that a projective module M is ⊕-cofinitely supplemented if and only if M is cofinitely semiperfect or briefly cof-semiperfect (i.e., each finitely generated factor module of M has a projective cover). In this paper we give various properties of the cof-semiperfect modules. If a projective module M is semiperfect then every M-generated module is cof-semiperfect. A ring R is semiperfect if and only if every free R-module is cof-semiperfect.

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Authors and Affiliations

  1. Ondokuz Mayis University, Amasya, Turkey

    H. Calisici

  2. Ondokuz Mayis University, Samsun, Turkey

    A. Pancar

Authors
  1. H. Calisici
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  2. A. Pancar
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Original Russian Text Copyright © 2005 Çalışıcı H. and Pancar A.

Translated from Sibirski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) Matematicheski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath}\) Zhurnal, Vol. 46, No. 2, pp. 460–465, March–April, 2005.

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Calisici, H., Pancar, A. Cofinitely semiperfect modules. Sib Math J 46, 359–363 (2005). https://doi.org/10.1007/s11202-005-0037-7

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  • DOI: https://doi.org/10.1007/s11202-005-0037-7

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