Open AccessGreen'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.