Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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HARMANCI INJECTIVITY OF MODULES

  • Ungor, Burcu (Department of Mathematics Ankara University)
  • Received : 2019.07.10
  • Accepted : 2020.03.25
  • Published : 2020.07.31
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Abstract

For the question "when is E(RR) a flat left R-module for any ring R?", in this paper, we deal with a class of modules partaking in the hierarchy of injective and cotorsion modules, so-called Harmanci injective modules, which turn out by the motivation of relations among the concepts of injectivity, flatness and cotorsionness. We give some characterizations and properties of this class of modules. It is shown that the class of all Harmanci injective modules is enveloping, and forms a perfect cotorsion theory with the class of modules whose character modules are Matlis injective. For the objective we pursue, we characterize when the injective envelope of a ring as a module over itself is a flat module.

Keywords

Acknowledgement

The author would like to thank the referee for careful reading and valuable suggestions to improve the presentation of this paper. The author also would like to thank Professor Harmanci for his contributions and inspiring comments. This paper would not have been possible without his support.

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