Sh. Asgari

Department of Mathematical Sciences‎, ‎University of Isfahan‎, ‎Isfahan‎, ‎Iran‎, ‎and School of Mathematics‎, ‎Institute for Research in Fundamental Sciences (IPM)‎, ‎Tehran‎, ‎Iran.

[ 1 ] - Rings for which every simple module is almost injective

We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-rin...

[ 2 ] - Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules

In this paper, we deal with solving systems of linear congruences over commutative CF-rings. More precisely, let R be a CF-ring (every finitely generated direct sum of cyclic R-modules has a canonical form) and let I_1,..., I_n be n ideals of R. We introduce congruence matrices theory techniques and exploit its application to solve the above system. Further, we investigate the application of co...