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Retractable and Coretractable Modules over Formal Triangular Matrix Rings

  • Derya Keskin Tütüncü
  • Rachid Tribak
Original Paper

Abstract

In this paper, we study retractable modules and coretractable modules over a formal triangular matrix ring \(T=\left[ \begin{array}{rr} A &{} 0 \\ M &{} B \\ \end{array} \right] \), where A and B are rings and M is a (BA)-bimodule. We determine necessary and sufficient conditions for a T-module to be, respectively, retractable or coretractable. We also characterize the right Kasch formal triangular matrix rings. Some examples are provided to illustrate and delimit our results.

Keywords

Coretractable modules Formal triangular matrix rings Right Kasch rings Retractable modules 

Mathematics Subject Classification

Primary 16D10 Secondary 16D20 16D70 16D80 16S50 

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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Department of MathematicsHacettepe UniversityAnkaraTurkey
  2. 2.Centre Régional des Métiers de L’Education et de la Formation (CRMEF)-TangerTangierMorocco

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