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Some Aspects of Graded Singular Submodules and Goldie Dimension |
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PP: 255-259 |
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Author(s) |
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Gayatri Das,
Helen K. Saikia,
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Abstract |
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| 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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