• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.589-599
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• 2012

An element of a ring is called strongly nil clean provided that it can be written as the sum of an idempotent and a nilpotent element that commute. We characterize, in this article, the strongly nil cleanness of $2{\times}2$ and $3{\times}3$ matrices over $R[x]/(x^2-1)$ where $R$ is a commutative local ring with characteristic 2. Matrix decompositions over fields are derived as special cases.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.51-58
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• 2009

Let R be a ring. A right R-module M is called perfect if M possesses a projective cover. In this paper, we consider the relationship between the class of perfect modules and other classes of modules. Some known rings are characterized by these relationships.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.903-913
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• 2007

A ring R has weakly stable range one provided that aR+bR=R implies that there exists a $y{\in}R$ such that $a+by{\in}R$ is right or left invertible. We prove, in this paper, that every regular element in an exchange ring having weakly stable range one is the sum of an idempotent and a weak unit. This generalize the corresponding result of one-sided unit-regular ring. Extensions of power comparability and power cancellation are also studied.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.701-708
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• 2018

In this paper, seminormality and t-closedness in ring extensions involving amalgamated algebras are studied. Let $R{\subseteq}T$ be a ring extension with ideals $I{\subseteq}J$, respectively such that J is contained in the conductor of R in T. Assume that T is integral over R. Then it is shown that ($R{\bowtie}I$, $T{\bowtie}J$) is a seminormal (resp., t-closed) pair if and only if (R, T) is a seminormal (resp., t-closed) pair.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.2
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• pp.1003-1019
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• 2019

Threshold ring signature scheme enables any t entities from N ring members to spontaneously generate a publicly verifiable t-out-of-N signature anonymously. The verifier is convinced that the signature is indeed generated by at least t users from the claimed group, but he cannot tell them apart. Threshold ring signatures are significant for ad-hoc groups such as mobile ad-hoc networks. Based on the lattice-based ring signature proposed by Melchor et al. at AFRICRYPT'13, this work presents a lattice-based threshold ring signature scheme, employing the technique of message block sharing proposed by Choi and Kim. Besides, in order to avoid the system parameter setup problems, we proposed a message processing technique called "pad-then-permute", to pre-process the message before blocking the message, thus making the threshold ring signature scheme more flexible. Our threshold ring signature scheme has several advantages: inherits the quantum immunity from the lattice structure; has considerably short signature and almost no signature size increase with the threshold value; provable to be correct, efficient, indistinguishable source hiding, and unforgeable.

• Journal of the Korean Institute of Gas
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• v.16 no.5
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• pp.52-57
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• 2012

This study presents sealing characteristics of multi-contact o-rings as functions of strain, compression stress, and contact normal stress using a FEM technique. The FEM results on the sealing characteristics show that the maximum strain, maximum compression stress, and maximum contact normal stress of multi-contact o-rings are approximately 1.7 times higher than those of conventional o-rings. This is due to a U-grooved cross section of multi-contact o-rings, and the multi-contact o-rings with a U-groove show more effective in sealing for high pressure vessels, valves, and gas equipments. And the extrusion failure in the multi- contact o-ring does not produce for an increased gas pressure due to a U-groove. This may extend sealing life compared to that of a conventional o-ring.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.257-269
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• 2009

A ring R is a weakly stable ring provided that aR + bR = R implies that there exists $y\;{\in}\;R$ such that $a\;+\;by\;{\in}\;R$ is right or left invertible. In this article, we characterize weakly stable rings by virtue of $2{\times}2$ invertible matrices over them. It is shown that a ring R is a weakly stable ring if and only if for any $A\;{\in}GL_2(R)$, there exist two invertible lower triangular L and K and an invertible upper triangular U such that A = LUK, where two of L, U and K have diagonal entries 1. Related results are also given. These extend the work of Nagarajan et al.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1775-1780
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• 2003

A hybrid finite element analysis was used to analyze the influence of ring gear rim thickness and spline number on the static properties of an epicyclic gear system with manufacturing errors. Both of these parameters affected the bearing force and critical stress. The effect of changes in the rim thickness on the load sharing between the gears depended on the type of manufacturing error. Ring flexibility improved the load sharing between planetary gears only in systems with planet tooth thickness or planet tangential errors; for other types of error, ring flexibility worsened the load sharing. To improve load sharing, rim thickness and spline number should be controlled within a specific range. The effect of the ring gear boundary condition was more apparent in a system with errors than in a normal system.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.1
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• pp.120-126
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• 2013

This paper proposes a novel scheme of fault detection and self-recovery for space-borne dual ring counters subject to transient faults. The considered ring counter is equipped with hardware redundancy, but it has a limited output domain where direct access to the current state is unavailable. We employ the theory of corrective control to detect any transient fault occurring to the counter bits and to realize immediate self-recovery of the ring counter back to the normal state. The structure of the fault-tolerant controller is designed to be minimal regardless of the counter size. To validate the applicability, we implement the proposed system on a commercial FGPA board.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.725-743
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• 2022

In this paper, the concepts of ω-linked homomorphisms, the ω_𝜙-operation, and DW_𝜙 rings are introduced. Also the relationships between ω_𝜙-ideals and ω-ideals over a ω-linked homomorphism 𝜙 : R → T are discussed. More precisely, it is shown that every ω_𝜙-ideal of T is a ω-ideal of T. Besides, it is shown that if T is not a DW_𝜙 ring, then T must have an infinite number of maximal ω_𝜙-ideals. Finally we give an application of Cohen's Theorem over ω-factor rings, namely it is shown that an integral domain R is an SM-domain with ω-dim(R) ≤ 1, if and only if for any nonzero ω-ideal I of R, (R/I)_ω is an Artinian ring, if and only if for any nonzero element α ∈ R, (R/(a))_ω is an Artinian ring, if and only if for any nonzero element α ∈ R, R satisfies the descending chain condition on ω-ideals of R containing a.