Green's Relations in Rings and Completely Simple Rings
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2018, Vol 14, Issue 2
Abstract
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.
Authors and Affiliations
Florion Cela
Keywords
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- EP ID EP651893
- DOI 10.24297/jam.v14i2.7781
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