• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.233-242
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• 2004

The aim of this note is to study properties of the generalized centroid of the semi-prime gamma rings. Main results are the following theorems: (1) Let M be a semi-prime $\Gamma$-ring and Q a quotient $\Gamma$-ring of M. If W is a non-zero submodule of the right (left) M-module Q, then $W\Gamma$W $\neq 0. Furthermore Q is a semi-prime $\Gamma$-ring. (2) Let M be a semi-prime $\Gamma$-ring and $C_{{Gamma}$ the generalized centroid of M. Then $C_{\Gamma}$ is a regular $\Gamma$-ring. (3) Let M be a semi-prime $\Gamma$-ring and $C_{\gamma}$ the extended centroid of M. If $C_{\gamma}$ is a $\Gamma$-field, then the $\Gamma$-ring M is a prime $\Gamma$-ring.

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.473-480
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• 2007

In this paper we define prime right ideals of semirings and prove that if every right ideal of a semiring R is prime then R is weakly regular. We also prove that if the set of right ideals of R is totally ordered then every right ideal of R is prime if and only if R is right weakly regular. Moreover in this paper we also define prime subsemimodule (generalizing the concept of prime right ideals) of an R-semimodule. We prove that if a subsemimodule K of an R-semimodule M is prime then $A_K(M)$ is also a prime ideal of R.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.445-453
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• 2020

Let R be a commutative semiring with identity and M be a unitary R-semimodule. Let 𝜙 : 𝒮(M) → 𝒮(M) ∪ {∅} be a function, where 𝒮(M) is the set of all subsemimodules of M. A proper subsemimodule N of M is called 𝜙-prime subsemimodule, if r ∈ R and x ∈ M with rx ∈ N \𝜙(N) implies that r ∈ (N :_R M) or x ∈ N. So if we take 𝜙(N) = ∅ (resp., 𝜙(N) = {0}), a 𝜙-prime subsemimodule is prime (resp., weakly prime). In this article we study the properties of several generalizations of prime subsemimodules.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.897-908
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• 2021

In this paper, we introduce the notion of pseudo 2-prime ideals in commutative rings. Let R be a commutative ring with a nonzero identity. A proper ideal P of R is said to be a pseudo 2-prime ideal if whenever xy ∈ P for some x, y ∈ R, then x²ⁿ ∈ Pⁿ or y²ⁿ ∈ Pⁿ for some n ∈ ℕ. Various examples and properties of pseudo 2-prime ideals are given. We also characterize pseudo 2-prime ideals of PID's and von Neumann regular rings. Finally, we use pseudo 2-prime ideals to characterize almost valuation domains (AV-domains).

• Journal of Korean Society of Steel Construction
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• v.16 no.3 s.70
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• pp.315-324
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• 2004

This study performs a yield line analysis of welded T-joints in cold-formed Square Hollow Sections (SHS) with the branch in axial compression. The existing yield line models proposed by Koto, Packer, Zhao, and CIDECT and the proposed yield line model of the previous study are compared, using the existing test results of welded T-joints in cold-formed SHS. The yield line model suggested in the previous paper, which is based on the simplified yield line analysis, is reviewed to evaluate its application limit on cold-formed SHS T-joints. In the proposed model, the round corner of the cold-formed SHS section and weld size are taken into account. Finally, the validity range of yield line analysis is determined by observing the actual failure modes and comparing the test value with the analysis value, set as ${\beta}^{\prime}{\leq}0.8$ where ${\beta}^{\prime}=0.8$, ${\beta}^{\prime}=b_1^{\prime}/b_0^{\prime}$, $b_1{^{\prime}}=b_1+t_0$ and $b_0{^{\prime}}=b_0-t_0$.

• Bulletin of the Korean Chemical Society
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• v.15 no.11
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• pp.1016-1019
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• 1994

• Applied Chemistry for Engineering
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• v.16 no.1
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• pp.45-51
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• 2005

$K^+-{\beta}^{{\prime}{\prime}}-Al_2O_3$ in the $K_2O-Li_2O-Al_2O_3$ ternary system was synthesized using aluminum nitrate solution as a starting material. For the synthesis of pure $K^+-{\beta}^{{\prime}{\prime}}-Al_2O_3$, raw materials with chemical composition of $0.84K_2O{\cdot}0.082Li_2O{\cdot}5.2Al_2O_3$ were mixed in solution state. The effects of dispersant and solution-pH were investigated in minimizing the particle size and on the synthesis of pure $K^+-{\beta}^{{\prime}{\prime}}-Al_2O_3$. Ethanol was used for a dispersant, and $NH_4OH$ solution and nitric acid were added for pH adjustment. The solution pH was increased from 1.0 to 7.5 by 0.5 increments. Each sample was calcined at $1200^{\circ}C$ for 2 h and characterized with X-ray diffraction and particle size analyzer. The pH of solution significantly effected both particle size and phase formation, while the addition of ethanol only effected particle size. The synthesis of pure $K^+-{\beta}^{{\prime}{\prime}}-Al_2O_3$ was favored by addition of nitric acid (for pH control).

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.49-64
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• 2020

In this paper, we define fuzzy prime ideals of C-algebras and investigate some of their properties. Furthermore, we study the topological properties of the space of fuzzy prime ideals of C-algebra equipped with the hull-kernel topology.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.217-221
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• 2005

Kehayopulu and Tsingelis [2] studied prime ideals of groupoids. Also the author studied prime left (right) ideals of groupoids. In this paper, we give some results on prime bi-ideals of groupoids.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.269-284
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• 2016

In this paper, we firstly use Krasnosel'skii fixed point theorem to investigate positive solutions for the following three-point boundary value problems for p-Laplacian with a parameter $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+{\lambda}f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1), λ > 0 is a parameter. Then we use Leggett-Williams fixed point theorem to study the existence of three positive solutions for the fractional boundary value problem $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1).