On Graded 2-Absorbing Primary Submodules

Çeli̇kel, Ece Yetki̇n

doi:10.12732/ijpam.v109i4.10

Cited by 9 publications

(5 citation statements)

References 3 publications

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“…Celikel in [10] extended graded 2-absorbing primary ideals to graded 2absorbing primary submodules. Recall from [10] that a proper graded submodule N of a graded R-module M is said to be a graded 2-absorbing primary submodule of M if whenever r g , s h ∈ h(R) and m λ ∈ h(M ) with r g s h m λ ∈ N, then r g s h ∈ (N : R M ) or r g m λ ∈ Gr M (N ) or s h m λ ∈ Gr M (N ).…”

Section: Introductionmentioning

confidence: 99%

On a generalization of graded 2-absorbing submodules

Al-Zoubi¹,

Alghueiri²

2023

MATHEMATICA

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"Let G be a group with identity e. Let R be a G-graded commutative ring with nonzero identity and M a graded R-module. In this paper, we introduce the concept of graded G2-absorbing submodule as a new generalization of a graded 2-absorbing submodule on the one hand and a generalization of a graded primary submodule on other hand. We give a number of results concerning these classes of graded submodules and their homogeneous components. In fact, our objective is to investigate graded G2-absorbing submodules and examine in particular when graded submodules are graded G2-absorbing submodules. For example, we give a characterization of graded G2-absorbing submodules. We also study the behaviour of graded G2-absorbing submodules under graded homomorphisms and under localization."

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Section: Introductionmentioning

confidence: 99%

On a generalization of graded 2-absorbing submodules

Al-Zoubi¹,

Alghueiri²

2023

MATHEMATICA

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“…s ∈ K or a ∈ Grad((K : R M))). As graded prime ideals (submodules) have an important role in graded ring (module) theory, several authors generalized these concepts in different ways, see ( [4][5][6][7][8]). Atani in [9] has introduced graded weakly prime submodules.…”

Section: Introductionmentioning

confidence: 99%

“…Al-Zoubi and Sharafat in [12] proposed the notion of graded 2-absorbing primary ideals, where a proper graded ideal I of R is called graded 2-absorbing primary if whenever x, y, z ∈ h(R) with xyz ∈ I, then xy ∈ I or xz ∈ Grad(I) or yz ∈ Grad(I). The notion of graded 2-absorbing primary submodules is studied in [7] as a generalization of graded 2-absorbing primary ideals. A proper graded R-submodule K of M is said to be a graded 2absorbing primary R-submodule (resp.…”

Section: Introductionmentioning

confidence: 99%

Graded ϕ-2-Absorbing and Graded ϕ-2-Absorbing Primary Submodules

2021

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The main goal of this article is to explore the concepts of graded ϕ-2-absorbing and graded ϕ-2-absorbing primary submodules as a new generalization of the concepts of graded 2-absorbing and graded 2-absorbing primary submodules. Let ϕ:GS(M)→GS(M)⋃{∅} be a function, where GS(M) denotes the collection of graded R-submodules of M. A proper K∈GS(M) is said to be a graded ϕ-2-absorbing R-submodule of M if whenever x,y are homogeneous elements of R and s is a homogeneous element of M with xys∈K−ϕ(K), then xs∈K or ys∈K or xy∈(K:RM), and we call K a graded ϕ-2-absorbing primary R-submodule of M if whenever x,y are homogeneous elements of R and s is a homogeneous element of M with xys∈K−ϕ(K), then xs or ys is in the graded radical of K or xy∈(K:RM). Several properties of these new forms of graded submodules are investigated.

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“…The concept of graded 2-absorbing submodules, as a generalization of graded prime submodules, was introduced by Al-Zoubi and Abu-Dawwas in [4] and studied in [8,9]. Then many generalizations of graded 2-absorbing submodules were studied such as graded 2-absorbing primary (see [19]), graded weakly 2-absorbing primary (see [7] ) and graded classical 2-absorbing submodule (see [6]).…”

Section: Introductionmentioning

confidence: 99%