Green's Relations in Rings and Completely Simple Rings


  • Florion Cela University of Tirana, Albania



In this paper we prove that which of Green's relations $\mathcal{L,R,H}$ and $\mathcal{D}$ in rings preserve the minimality of quasi-ideal. By this it is possible to show the structure of the classes generated by the above relations which have a minimal quasi ideal. For the completely simple rings we show that they are generated by the union of zero with a $\mathcal{D} $-class. Also we emphasize that a completely simple ring coincides with the union of zero with a $\mathcal{D} $-class if and only if it is a division ring.


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Author Biography

Florion Cela, University of Tirana, Albania

Faculty of Natural and Sciences. University of Tirana, Albania


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How to Cite

Cela, F. (2018). Green’s Relations in Rings and Completely Simple Rings. JOURNAL OF ADVANCES IN MATHEMATICS, 14(2), 7965–7974.