• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.217-231
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• 2009

The notion of *-medial pseudo BCI-algebras is introduced, and its characterization is discussed. The concepts of associative pseudo ideals (resp. pseudo p-ideals, pseudo q-ideals and pseudo a-ideals) are introduced, and related properties are investigated. Conditions for a pseudo ideal to be a pseudo p-ideal (resp. pseudo q-ideal) are provided. A characterization of an associative pseudo ideal is given. We finally show that every pseudo BCI-homomorphic image and preimage of an associative pseudo ideal (resp. a pseudo p-ideal, a pseudo q-ideal and a pseudo a-ideal) is also an associative pseudo ideal (resp. a pseudo p-ideal, a pseudo q-ideal and a pseudo a-ideal).

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.795-807
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• 2009

The concepts of fuzzy pseudo ideals (resp. fuzzy pseudo p-ideals, associative fuzzy pseudo ideals, fuzzy pseudo q-ideals and fuzzy pseudo a-ideals) in a pseudo BCI-algebra are introduced, and related properties are investigated. Conditions for a fuzzy pseudo ideal to be a fuzzy pseudo p-ideal (resp. fuzzy pseudo q-ideal) are provided. A characterization and properties of an associative fuzzy pseudo ideal are given.

• 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).

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.935-946
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• 2015

The purpose of this paper is to introduce a new class of rings that is closely related to the classes of pseudo valuation rings (PVRs) and pseudo-almost valuation domains (PAVDs). A commutative ring R is said to be ${\phi}$-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map ${\phi}$ from the total quotient ring T(R) to R localized at Nil(R). A prime ideal P of a ${\phi}$-ring R is said to be a ${\phi}$-pseudo-strongly prime ideal if, whenever $x,y{\in}R_{Nil(R)}$ and $(xy){\phi}(P){\subseteq}{\phi}(P)$, then there exists an integer $m{\geqslant}1$ such that either $x^m{\in}{\phi}(R)$ or $y^m{\phi}(P){\subseteq}{\phi}(P)$. If each prime ideal of R is a ${\phi}$-pseudo strongly prime ideal, then we say that R is a ${\phi}$-pseudo-almost valuation ring (${\phi}$-PAVR). Among the properties of ${\phi}$-PAVRs, we show that a quasilocal ${\phi}$-ring R with regular maximal ideal M is a ${\phi}$-PAVR if and only if V = (M : M) is a ${\phi}$-almost chained ring with maximal ideal $\sqrt{MV}$. We also investigate the overrings of a ${\phi}$-PAVR.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.65-77
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• 2020

In this paper, for any non-empty subsets A, I of a pseudo BCI-algebra X, we introduce the concept of pseudo p-closure of A with respect to I, denoted by A^pc_I, and investigate some related properties. Applying this concept, we state a necessary and sufficient condition for a pseudo BCI-algebra 1) to be a p-semisimple pseudo BCI-algebra; 2) to be a pseudo BCK-algebra. Moreover, we show that A^pc_{0} is the least positive pseudo ideal of X containing A, and characterize it by the union of some branches. We also show that the set of all pseudo ideals of X which A^pc_I = A, is a complete lattice. Finally, we prove that this notion can be used to define a closure operation.

• Journal of the Korean Mathematical Society
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• v.61 no.5
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• pp.953-973
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• 2024

Let R = ⊕_α∈Γ R_α be a commutative ring graded by an arbitrary torsionless monoid Γ. A homogeneous prime ideal P of R is said to be strongly homogeneous prime if aP and bR are comparable for any homogeneous elements a, b of R. We will say that R is a graded pseudo-valuation ring (gr-PVR for short) if every homogeneous prime ideal of R is strongly homogeneous prime. In this paper, we introduce and study the graded version of the pseudo-valuation rings which is a generalization of the gr-pseudo-valuation domains in the context of arbitrary Γ-graded rings (with zero-divisors). We then study the possible transfer of this property to the graded trivial ring extension and the graded amalgamation. Our goal is to provide examples of new classes of Γ-graded rings that satisfy the above mentioned property.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.185-193
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• 2010

Let D be an integral domain, and let ${\bar{D}}$ be the integral closure of D. We show that if D is an almost pseudo-valuation domain (APVD), then D is a quasi-$Pr{\ddot{u}}fer$ domain if and only if D=P is a quasi-$Pr{\ddot{u}}fer$ domain for each prime ideal P of D, if and only if ${\bar{D}}$ is a valuation domain. We also show that D(X), the Nagata ring of D, is a locally APVD if and only if D is a locally APVD and ${\bar{D}}$ is a $Pr{\ddot{u}}fer$ domain.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.1
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• pp.21-32
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• 2002

In this paper, for any prime q, new cyclic difference sets with Singer parameter equation omitted are constructed by using the q-ary sequences (d-homogeneous functions) of period $q_n$-1. When q is a power of 3, new cyclic difference sets with Singer parameter equation omitted are constructed from the ternary sequences of period $q_n$-1 with ideal autocorrealtion found by Helleseth, Kumar and Martinsen.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.4
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• pp.659-665
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• 2017

Power semiconductor devices required the low on-resistance and high breakdown voltage. Wide band-gap materials opened a new technology of the power devices which promised a thin drift layer at an identical breakdown voltage. The diamond had the wide band-gap of 5.5 eV which induced the low power loss, high breakdown capability, low intrinsic carrier generation, and high operation temperature. We investigated the p-type pseudo-vertical diamond Schottky barrier diodes using a numerical simulation. The impact ionization rate was material to calculating the breakdown voltage. We revised the impact ionization rate of the diamond for adjusting the parallel-plane breakdown field at 10 MV/cm. Effects of the field plate on the breakdown voltage was also analyzed. A conventional diamond Schottky barrier diode without field plate exhibited the high forward current of 0.52 A/mm and low on-resistance of $1.71{\Omega}-mm$ at the forward voltage of 2 V. The simulated breakdown field of the conventional device was 13.3 MV/cm. The breakdown voltage of the conventional device and proposed devices with the $SiO_2$ passivation layer, anode field plate (AFP), and cathode field plate (CFP) was 680, 810, 810, and 1020 V, respectively. The AFP cannot alleviate the concentration of the electric field at the cathode edge. The CFP increased the breakdown voltage with evidences of the electric field and potential. However, we should consider the dielectric breakdown because the ideal breakdown field of the diamond is higher than that of the $SiO_2$, which is widely used as the passivation layer. The real breakdown voltage of the device with CFP decreased from 1020 to 565 V due to the dielectric breakdown.