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