Prime structures in a Morita context

Abstract

In this paper, we study the primeness and semiprimeness of a Morita context. Necessary and sufficient conditions are investigated for an ideal of a Morita context to be a prime ideal and a semiprime ideal. In particular, we determine the conditions under which a Morita context is prime and semiprime.

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Acknowledgements

The authors would like to thank the referee for his/her valuable suggestions which contributed to improve the presentation of this paper. The first author thanks the Scientific and Technological Research Council of Turkey (TUBITAK) for the financial support.

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Correspondence to Mete Burak Calci.

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Calci, M.B., Halicioglu, S., Harmanci, A. et al. Prime structures in a Morita context. Bol. Soc. Mat. Mex. 26, 991–1001 (2020). https://doi.org/10.1007/s40590-020-00295-y

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Keywords

  • Morita context
  • Prime ideal
  • Semiprime ideal
  • Prime radical
  • Prime ring
  • Semiprime ring

Mathematics Subject Classification

  • 16D80
  • 16S50
  • 16S99