##### 1. A GRAPH WHICH RECOGNIZES IDEMPOTENTS OF A COMMUTATIVE RING

H. Dorbidi; S. Alikhani

Volume 7, Issue 2 , Winter and Spring 2020, , Pages 143-154

##### 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 ...  Read More

##### 2. SOME REMARKS ON ALMOST UNISERIAL RINGS AND MODULES

H. R. Dorbidi

Volume 5, Issue 1 , Summer and Autumn 2017, , Pages 65-72

##### Abstract
In this paper we study almost uniserial rings and modules. An R−module M is called almost uniserial if any two nonisomorphic submodules are linearly ordered by inclusion. A ring R is an almost left uniserial ring if R_R is almost uniserial. We give some necessary and sufficient condition for an ...  Read More