@article { author = {Dorbidi, H. and Alikhani, S.}, title = {A GRAPH WHICH RECOGNIZES IDEMPOTENTS OF A COMMUTATIVE RING}, journal = {Journal of Algebraic Systems}, volume = {7}, number = {2}, pages = {143-154}, year = {2020}, publisher = {Shahrood University of Technology}, issn = {2345-5128}, eissn = {2345-511X}, doi = {10.22044/jas.2019.7405.1365}, abstract = {In this paper we introduce and study a graph on the set of ideals of a commutative ring $R$. The vertices of this graph are non-trivial ideals of $R$ and two distinct ideals $I$ and $J$ are adjacent if and only $IJ=I\cap J$. We obtain some properties of this graph and study its relation to the structure of $R$.}, keywords = {Graph,diameter,Ring,Idempotent}, url = {https://jas.shahroodut.ac.ir/article_1585.html}, eprint = {https://jas.shahroodut.ac.ir/article_1585_0115d6f468b7fb69d3639428ff331638.pdf} }