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Extension of Almost Primary Ideals to Noncommutative Rings and the Generalization of Nilary Ideals
Mathematics, 2023 In this paper, we introduce the concepts of almost right primary ideals and almost nilary ideals and study their related results. We compare almost right primary ideals with other types of ideals, such as right primary ideals and weakly right primary ...
Alaa Abouhalaka, Şehmus Fındık
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Primary Ideals and Their Differential Equations [PDF]
Foundations of Computational Mathematics, 2021 An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE. This paper develops a novel structure theory for primary ideals in a polynomial ring.
Yairon Cid-Ruiz +2 more
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On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 This paper introduces a subset of the set of 1-absorbing primary ideals introduced in [3]. An ideal I of a ring R is (1,2)-absorbing primary if, whenever non-unit elements α, β, γ ∈ R with αβγ ∈ I,then αβ ∈ I or γ2 ∈ I.
Alhazmy Khaled +3 more
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Applications of Fuzzy Semiprimary Ideals under Group Action
Axioms, 2023 Group actions are a valuable tool for investigating the symmetry and automorphism features of rings. The concept of fuzzy ideals in rings has been expanded with the introduction of fuzzy primary, weak primary, and semiprimary ideals.
Asma Ali, Amal S. Alali, Arshad Zishan
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Mathematics, 2021 The purpose of this paper is to introduce the concept of graded 2-prime ideals as a new generalization of graded prime ideals. We show that graded 2-prime ideals and graded semi-prime ideals are different.
Malik Bataineh, Rashid Abu-Dawwas
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Mathematics, 2021 Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that P⋂S=∅.
Azzh Saad Alshehry
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Graded weakly 1-absorbing primary ideals
Demonstratio Mathematica, 2023 Let GG be a group and RR be a GG-graded commutative ring with nonzero unity 1. In this article, we introduce the concept of graded weakly 1-absorbing primary ideals which is a generalization of graded 1-absorbing primary ideal.
Bataineh Malik, Abu-Dawwas Rashid
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On 1-absorbing δ-primary ideals
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Let R be a commutative ring with nonzero identity. Let 𝒥(R) be the set of all ideals of R and let δ : 𝒥 (R) → 𝒥 (R) be a function. Then δ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J ⊆ I, we have L ⊆ δ (L) and
Khalfi Abdelhaq El +3 more
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ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS [PDF]
Journal of Algebraic Systems, 2020 We study primary ideals of the ring $mathcal{R}L$ of real-valued continuous functions on a completely regular frame $L$. We observe that prime ideals and primary ideals coincide in a $P$-frame.
M. Abedi
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Radicals of Generalized Prime Ideals in Ternary Semigroups
Discussiones Mathematicae - General Algebra and Applications, 2022 In this paper, the concepts of f-prime ideals and f-semiprime ideals on a ternary semigroup are considered as a generalization of pseudo prime ideals and pseudo semiprime ideals, respectively.
Satvong Narakon +2 more
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