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...
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