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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 4 > No. 3


Some Aspects of Graded Singular Submodules and Goldie Dimension

PP: 255-259
Gayatri Das, Helen K. Saikia,
In this paper we attempt to study singular submodules and Goldie dimension of modules in graded case. We investigate various aspects of graded torsion submodules and graded singular submodules of a graded module. If M is graded module over a ring R then it is seen that under certain conditions Tg(M), the graded torsion submodule of M coincides with Zg(M), the graded singular submodule of M.We establish some characteristics of graded singular submodules. Defining graded singularity rank function s−rR(M) as the Goldie dimension of M modulo ZR(M). We prove that s−rR(M) = s−rR(K)+s−rR(M/K), where K is a graded submodule of M and M a graded right R- module with finite Goldie dimension showing thereby that graded singularity rank function is additive.

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