Graded Essential Extensions and Graded Injective Modules
Pure and Applied Mathematics Journal
Volume 4, Issue 2, April 2015, Pages: 47-51
Received: Jan. 20, 2015; Accepted: Feb. 6, 2015; Published: Feb. 11, 2015
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Authors
Salah El Din S. Hussein, Department of Mathematics, Faculty of Science, Ain Shams University, Abasaya-Cairo, Egypt
Essam El Seidy, Department of Mathematics, Faculty of Science, Ain Shams University, Abasaya-Cairo, Egypt
H. S. Diab, Department of Mathematics, Faculty of Science, Ain Shams University, Abasaya-Cairo, Egypt
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Abstract
In this paper we establish the relation between graded essential extensions of graded modules and injectivity of such modules. We relate the graded injective hull Egr (M) of a graded module M with the graded essential extensions of M. We round off by establishing necessary and sufficient conditions for indecomposability of graded injective modules in terms of their graded injective hulls.
Keywords
Graded Injective Module, Graded Essential Extension, Graded Injective Hull
To cite this article
Salah El Din S. Hussein, Essam El Seidy, H. S. Diab, Graded Essential Extensions and Graded Injective Modules, Pure and Applied Mathematics Journal. Vol. 4, No. 2, 2015, pp. 47-51. doi: 10.11648/j.pamj.20150402.13
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