Green's Relations in Rings and Completely Simple Rings | Zendy

Florion Cela | Zendy

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Green's Relations in Rings and Completely Simple Rings

Author(s) -

Florion Cela

Publication year - 2018

Publication title -

journal of advances in mathematics

Language(s) - English

Resource type - Journals

ISSN - 2347-1921

DOI - 10.24297/jam.v14i2.7781

Subject(s) - mathematics , simple (philosophy) , ideal (ethics) , zero (linguistics) , class (philosophy) , ring (chemistry) , simple ring , combinatorics , maximal ideal , pure mathematics , discrete mathematics , commutative ring , principal ideal ring , law , philosophy , linguistics , chemistry , organic chemistry , epistemology , artificial intelligence , commutative property , political science , computer science

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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