• 대한수학회논문집
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• 제32권4호
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• pp.811-826
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• 2017

The reversible property of rings was initially introduced by Habeb and plays a role in noncommutative ring theory. In this note we study the reversible ring property on nilpotent elements, introducing the concept of commutativity of nilpotent elements at zero (simply, a CNZ ring) as a generalization of reversible rings. We first find the CNZ property of 2 by 2 full matrix rings over fields, which provides a basis for studying the structure of CNZ rings. We next observe various kinds of CNZ rings including ordinary ring extensions.

• 대한수학회보
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• 제48권1호
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• pp.115-127
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• 2011

We study the structure of the set of nilpotent elements in various kinds of ring and introduce the concept of NR ring as a generalization of Armendariz rings and NI rings. We determine the precise relationships between NR rings and related ring-theoretic conditions. The Kothe's conjecture is true for the class of NR rings. We examined whether several kinds of extensions preserve the NR condition. The classical right quotient ring of an NR ring is also studied under some conditions on the subset of nilpotent elements.

• 대한수학회보
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• 제53권5호
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• pp.1309-1325
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• 2016

This note focuses on a ring property in which upper and lower nilradicals coincide, as a generalizations of symmetric rings. The concept of symmetric ideal and ring in the noncommutative ring theory was initially introduced by Lambek, as an extension of the usual commutative ideal theory. The investigation of symmetric rings provided many useful results to the study in the noncommutative ring theory. So the results obtained from this study may be applicable to observing the structure of zero divisors in various kinds of algebraic systems containing matrix rings and polynomial rings.

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.363-372
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• 2007

An element $a$ in a ring R is called left morphic if $$R/Ra{\simeq_-}1(a)$$. A ring is called left morphic if every element is left morphic. In this paper, an element $a$ in a ring R is called left ${\pi}$-morphic (resp. left G-morphic) if there exists a positive number $n$ such that $a^n$ (resp. $a^n{\neq}0$) is left morphic. A ring R is called left ${\pi}$-morphic (resp. left G-morphic) if every element is left ${\pi}$-morphic (resp. left G-morphic). The Morita invariance of left ${\pi}$-morphic (resp. left G-morphic) rings is discussed. Several relevant properties are proved. In particular, it is shown that a left Noetherian ring R with $M_4(R)$ left G-morphic or $M_2(R)$ left morphic is QF. Some known results of left morphic rings are extended to left G-morphic rings and left ${\pi}$-morphic rings.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.127-132
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• 2007

In this paper, we show that if R is a commutative ring with identity and (S, ${\leq}$) is a strictly totally ordered monoid, then the ring [[$R^{S,{\leq}}$]] of generalized power series is a PF-ring if and only if for any two S-indexed subsets A and B of R such that $B{\subseteq}ann_R(|A)$, there exists $c{\in}ann_R(A)$ such that $bc=b$ for all $b{\in}B$, and that for a Noetherian ring R, $[[R^{S,{\leq}}$]] is a PP ring if and only if R is a PP ring.

• 소성∙가공
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• 제16권4호
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• pp.223-228
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• 2007

The profile ring rolling process of Ti-6Al-4V alloy was investigated by finite element(FE) simulation and experimental analysis. The process design of the profile ring rolling includes geometry design and optimization of process variables. The geometry design such as initial billet and blank sizes, and final rolled ring shape was carried out with the calculation method based on the uniform deformation concept between the wall thickness and ring height. FEM simulation was used to calculate the state variables such as strain, strain rate and temperature and to predict the formation of forming defects during ring rolling process. Finally, the mechanical properties of profiled Ti-6Al-4V alloy ring product were analyzed with the evolution of microstructures during the ring rolling process.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2006년도 춘계학술대회논문집
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• pp.1142-1148
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• 2006

The floating ring seal which is used in the high pressure turbo pump is frequently used in the oxidizer pump and the fuel pump of the turbo pump of the liquid propulsion rocket, because it is able to minimize clearance to decrease the leakage flow rate. But, floating ring seal has a tendency to increase the force which caused instability of system as the eccentricity ratio increases. In this paper, we devised design of floating ring seal which decrease contact area between floating and supporting ring. Modified floating ring seal has a tendency to decrease the eccentricity ratio compare with original floating ring seal. The whirl frequency ratio which is able to distinguish stability of system decrease compare with original floating ring seal

• 산업공학
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• 제9권3호
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• pp.64-71
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• 1996

In the survivability and simplicity aspect, SONET Self-healing Ring(SHR) is one of the most important schemes for the high-speed telecommunication networks. Since the ring capacity requirement is defined by the largest STS-1 cross-section in the ring, load balancing is the key issue in the design of SONET SHR. Recently, most of the research on load balancing problem have been concentrated on the SONET single-ring case. However, in certain applications, multiple-ring configuration is necessary because of the geographical limitations or the need for extra bandwidth. In this paper, the load balancing problem for SONET dual-ring is considered by assuming symmetric inter-ring demands. We present a linear programming based formulation of the problem. Initial solution and improvement procedures are presented, which solves the routing and interconnection between the two rings for each demand. Computational experiments are performed on various size of networks with randomly generated demand sets. Results show that the proposed algorithm is excellent in both the solution quality and the computational time requirement. The average error bound of the solutions obtained is 0.26% of the optimum.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.397-406
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• 2013

A ring R is called a left (right) SF-ring if simple left (right) R-modules are flat. It is still unknown whether a left (right) SF-ring is von Neumann regular. In this paper, we give some conditions for a left (right) SF-ring to be (a) von Neumann regular; (b) strongly regular; (c) division ring. It is proved that: (1) a right SF-ring R is regular if maximal essential right (left) ideals of R are weakly left (right) ideals of R (this result gives an affirmative answer to the question raised by Zhang in 1994); (2) a left SF-ring R is strongly regular if every non-zero left (right) ideal of R contains a non-zero left (right) ideal of R which is a W-ideal; (3) if R is a left SF-ring such that $l(x)(r(x))$ is an essential left (right) ideal for every right (left) zero divisor x of R, then R is a division ring.

• 한국가구학회지
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• 제23권4호
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• pp.479-484
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• 2012

Tree-ring dating can be used to date scientifically prehistoric timbers, historical buildings or woodcrafts. It gives a calendar year to each tree ring and produces the felling dates of logs or wood panels. In this study, we applied tree-ring dating to a medicine cabinet in Seoul Museum of History. We obtained tree-ring data from radial or cross section by taking photographs with a digital camera. The cabinet were dated A.D. 1821 to the last ring. It was about 50 year older than the previous medicine cabinets. Tree-ring patterns indicated that the origin of woods for the cabinet would be near Sorak mountains.