Finiteness Conditions for Modules

Anderson, Frank W.; Fuller, Kent R.

doi:10.1007/978-1-4684-9913-1_4

Cited by 2 publications

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“…(𝒊𝒗) ⟹ (𝒊𝒊) Analogous to (𝑖𝑖𝑖) ⟹ (𝑖).  Additionally, similar to the previous outcome, if it is possible to hypothesis that 𝐻 ∈ Mod-ℛ has a finite decomposition 𝐻 =⊕ 𝑡=1𝑚 𝐻 𝑡 such that 𝐸𝑛𝑑 𝑅 (𝐻 𝑡 ) is local for all 𝑡 = 1,2, … , 𝑚, this implies 𝐻 𝑅 is an indecomposable decomposition see[17, Theorem 12.6], and we arrive at a similar conclusion.The decomposition of ⨁-g-supplemented modules will be investigated next. Let 𝐻 ∈ 𝐷𝐺𝑆, then we can write 𝐻 = 𝐻 1 ⨁𝐻 2 where 𝐻 1 ∈ Mod-ℛ with 𝑅𝑎𝑑 𝑔 (𝐻 1 ) ↪ 𝑔𝑠 𝐻 1 and 𝐻 2 ∈ Mod-ℛ with 𝑅𝑎𝑑 𝑔 (𝐻 2 ) = 𝐻 2 .…”

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Some Generalizations of g-lifting Modules

Ghawi

2023

J. Al-Qadisiyah Comp. Sci. Math.

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In this work we will attempt to define and investigate new classes of modules named -g-supplemented and -g-radical supplemented as a proper generalization of class of g-lifting modules and identify several distinct characterizations of these modules. Additionally, we'll attempt to explain the concepts of projective g-covers and g-semiperfect modules. It is shown that the two buildings of g-semiperfect and -g-supplemented modules are the same for the class of projective modules.

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“…Summands and decompositions of modules with ⨁-g-radical supplements are covered in Section 6. You can find the ideas that are not covered here in [17,2].…”

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Some Generalizations of g-lifting Modules

Ghawi

2023

J. Al-Qadisiyah Comp. Sci. Math.

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“…Suppose as a commutative ring with is closed with direct products. So the following are equivalent: (1) As been an SJ-injective -module.…”

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Sj-Flat Modules

Medhloom JUDDAH

2022

MINAR Journal

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In this work we are aiming to explain the notion of SJ-flat Modules. SJ-injectivity notion had been proposed and examined within R-module right M characterised as SJ-N-injective – as N stands for R-module right– while R-homomorphism out of a right submodule for SJ(N)=soc(N) (J(N)J(R)) within M in an extend till N. Examples showing how SJ-injectivity differs from previous injectivity ideas like nonobjectivity and soc-injectivity are offered to show how this new injectivity condition is linked to existing injectivity notions. Highlighted are a few characteristics of the new injectivity class

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Finiteness Conditions for Modules

Cited by 2 publications

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Some Generalizations of g-lifting Modules

Some Generalizations of g-lifting Modules

Sj-Flat Modules

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