On graded Ie-prime submodules of graded modules over graded commutative rings
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Let G be a group with identity e. Let R be a G-graded commutative ring with identity and M a graded R-module. We introduce the concept of graded Ie-prime submodule as a generalization of a graded prime submodule for I =?g?G Ig a fixed graded ideal of R. We give a number of results concerning this class of graded submodules and their homogeneous components. A proper graded submodule N of M is said to be a graded Ie-prime submodule of M if whenever rg ? h(R) and mh ? h(M) with rgmh ? N ? IeN, then either rg ? (N :R M) or mh ? N.
2021 ◽
Vol 10
(11)
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pp. 3479-3489
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2015 ◽
Vol 08
(02)
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pp. 1550016
2017 ◽
Vol 37
(1)
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pp. 153-168
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2009 ◽
Vol 52
(2)
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pp. 253-259
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2019 ◽
Vol 32
(2)
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pp. 103
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2001 ◽
Vol 43
(1)
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pp. 103-111
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