• Title, Summary, Keyword: directly finite ring

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ON COMMUTATIVITY OF REGULAR PRODUCTS

  • Kwak, Tai Keun;Lee, Yang;Seo, Yeonsook
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1713-1726
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    • 2018
  • We study the one-sided regularity of matrices in upper triangular matrix rings in relation with the structure of diagonal entries. We next consider a ring theoretic condition that ab being regular implies ba being also regular for elements a, b in a given ring. Rings with such a condition are said to be commutative at regular product (simply, CRP rings). CRP rings are shown to be contained in the class of directly finite rings, and we prove that if R is a directly finite ring that satisfies the descending chain condition for principal right ideals or principal left ideals, then R is CRP. We obtain in particular that the upper triangular matrix rings over commutative rings are CRP.

A STRUCTURE OF NONCENTRAL IDEMPOTENTS

  • Cho, Eun-Kyung;Kwak, Tai Keun;Lee, Yang;Piao, Zhelin;Seo, Yeon Sook
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.25-40
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    • 2018
  • We focus on the structure of the set of noncentral idempotents whose role is similar to one of central idempotents. We introduce the concept of quasi-Abelian rings which unit-regular rings satisfy. We first observe that the class of quasi-Abelian rings is seated between Abelian and direct finiteness. It is proved that a regular ring is directly finite if and only if it is quasi-Abelian. It is also shown that quasi-Abelian property is not left-right symmetric, but left-right symmetric when a given ring has an involution. Quasi-Abelian property is shown to do not pass to polynomial rings, comparing with Abelian property passing to polynomial rings.

SYMMETRIC PROPERTY OF RINGS WITH RESPECT TO THE JACOBSON RADICAL

  • Calci, Tugce Pekacar;Halicioglu, Sait;Harmanci, Abdullah
    • Communications of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.43-54
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    • 2019
  • Let R be a ring with identity and J(R) denote the Jacobson radical of R, i.e., the intersection of all maximal left ideals of R. A ring R is called J-symmetric if for any $a,b,c{\in}R$, abc = 0 implies $bac{\in}J(R)$. We prove that some results of symmetric rings can be extended to the J-symmetric rings for this general setting. We give many characterizations of such rings. We show that the class of J-symmetric rings lies strictly between the class of symmetric rings and the class of directly finite rings.

ON A GENERALIZATION OF THE MCCOY CONDITION

  • Jeon, Young-Cheol;Kim, Hong-Kee;Kim, Nam-Kyun;Kwak, Tai-Keun;Lee, Yang;Yeo, Dong-Eun
    • Journal of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1269-1282
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    • 2010
  • We in this note consider a new concept, so called $\pi$-McCoy, which unifies McCoy rings and IFP rings. The classes of McCoy rings and IFP rings do not contain full matrix rings and upper (lower) triangular matrix rings, but the class of $\pi$-McCoy rings contain upper (lower) triangular matrix rings and many kinds of full matrix rings. We first study the basic structure of $\pi$-McCoy rings, observing the relations among $\pi$-McCoy rings, Abelian rings, 2-primal rings, directly finite rings, and ($\pi-$)regular rings. It is proved that the n by n full matrix rings ($n\geq2$) over reduced rings are not $\pi$-McCoy, finding $\pi$-McCoy matrix rings over non-reduced rings. It is shown that the $\pi$-McCoyness is preserved by polynomial rings (when they are of bounded index of nilpotency) and classical quotient rings. Several kinds of extensions of $\pi$-McCoy rings are also examined.

Finite Element Analysis of Residual Stress after Quenching and Element Removal of A1 Ring Rolls (알루미늄 링롤재의 급냉 및 요소제거 후 잔류응력의 유한요소해석)

  • 박성한;구송회;이방업;조원만;은일상
    • Journal of the Korean Society of Propulsion Engineers
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    • v.2 no.1
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    • pp.31-40
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    • 1998
  • To predict residual stresses of aluminum ring rolls after quenching and element removal, 2-D and 3-D thermal elasto-plastic analyses were performed. Strains measured by three step sectioning method were directly compared to those analysed using ABAQUS's element removal. Numerical residual stresses after quenching had similar tendency to measured ones after 2 step aging, but the difference between numerical and measured ones was large. The difference is the reason why there are nonuniform residual stress distributions to ring height direction due to small height of ring, It is judged that the increase of ring height will improve the accuracy of measured ones and decrease the difference. By direct comparison between 3-D numerical strains to simulate three step sectioning method and measured ones, the accuracy of measurement and analysis can be improved. It is concluded that there can be predicted the deformation behavior on machining complex shaped large structures with residual stresses.

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Development of Stress Intensity Factor Equation for the Notched Ring Test (NRT) Specimen (Notched Ring Test 저속균열 시험편의 응력확대계수정식화)

  • Pyo, Sooho;Choi, Sunwoong
    • Korean Journal of Materials Research
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    • v.24 no.2
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    • pp.87-92
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    • 2014
  • The Notched Ring Test(NRT) has proven to be very useful in determining the slow crack growth behavior of polyethylene pressure pipes. In particular, the test is simple and an order of magnitude shorter in experimental times as compared to the currently used Notched Pipe Test(NPT), which makes this method attractive for use as the accelerated slow crack growth test. In addition, since the NRT specimen is taken directly from the pipe, having maintained the cross-section, processing induced artifacts that would affect the slow crack growth behavior are not altered. This makes the direct comparison to the slow crack growth specimen in pipe from more meaningful. In this study, for comparison with other available slow crack growth methods, including the NPT, the stress intensity factor equation for NRT specimen was developed and demonstrated of its accuracy within 3% of that obtained from the finite element analysis. The equation was derived using a flexure formula of curved beam bending along with numerically determined geometric factors. The accuracy of the equation was successfully tested on 63, 110, 140, 160, 250, and 400 mm nominal pipe diameters, with crack depth ranging from 15 % to 45 % of the pipe wall thickness, and for standard dimensional ratio(SDR) of 9, 11, and 13.6. Using this equation the slow crack results from 110SDR11 NRT specimen were compared to that from the NPT specimen, which demonstrated that the NRT specimen was equivalent to the NPT specimen in creating the slow crack, however in much shorter experimental times.

Weakly np-Injective Rings and Weakly C2 Rings

  • Wei, Junchao;Che, Jianhua
    • Kyungpook Mathematical Journal
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    • v.51 no.1
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    • pp.93-108
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    • 2011
  • A ring R is called left weakly np- injective if for each non-nilpotent element a of R, there exists a positive integer n such that any left R- homomorphism from $Ra^n$ to R is right multiplication by an element of R. In this paper various properties of these rings are first developed, many extending known results such as every left or right module over a left weakly np- injective ring is divisible; R is left seft-injective if and only if R is left weakly np-injective and $_RR$ is weakly injective; R is strongly regular if and only if R is abelian left pp and left weakly np- injective. We next introduce the concepts of left weakly pp rings and left weakly C2 rings. In terms of these rings, we give some characterizations of (von Neumann) regular rings such as R is regular if and only if R is n- regular, left weakly pp and left weakly C2. Finally, the relations among left C2 rings, left weakly C2 rings and left GC2 rings are given.

Influence of the Flow Stress of the Rivet on the Numerical Prediction of the Self-Piercing Rivet (SPR) Joining (Self-Piercing Rivet 접합공정의 수치예측에 미치는 리벳 유동응력의 영향)

  • Kim, S.H.;Bae, G.;Song, J.H.;Park, K.Y.;Park, N.
    • Transactions of Materials Processing
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    • v.29 no.5
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    • pp.257-264
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    • 2020
  • This paper is concerned with the influence of the plastic property of the rivet on the numerical prediction of the Self-Piercing Rivet (SPR) Joining. In order to predict the plastic property of the rivet, a ring compression specimen was directly fabricated from the rivet used for the mechanical joining of dissimilar materials, and the FE analysis together with the ring compression test was iteratively carried out by changing the plastic property of the rivet. For reliable FE analysis, a friction coefficient was estimated based on a friction calibration curve, measuring the reductions in inner diameter and height of the ring specimen after the compression test. From each simulation result, the force-displacement curves were then compared from each other so as to obtain the rivet plastic property that shows good agreement with the experimental result. The SPR joining between GA590 1.0t and Al5052 2.0t was conducted, and the numerical prediction was performed with the use of the plastic property evaluated based on the inverse analysis and the one referred from Mori et al. [11]. Comparison of the experiment and the numerical predictions in terms of the interlock and bottom thickness revealed that the reliable evaluation of the plastic property of the rivet is necessary for the trustworthy numerical prediction of the SPR joining.

Vibration Analysis of Bladed Disk using Non-contact Blade Vibration System

  • Joung, Kyu-Kang;Han, Chak-Heui;Kang, Suk-Chul;Kim, Yeong-Ryeon
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • pp.871-876
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    • 2008
  • The blade vibration problem of bladed disk is the most critical subject to consider since it directly affects the stable performance of the engine as well as life of the engine. Especially, due to complicated vibration pattern of the bladed disk, more effort was required for vibration analysis and test. The research of measuring the vibration of the bladed disk, using NSMS(Non-intrusive stress measurement) instead of Aeromechanics testing method requiring slip ring or telemetry system with strain gauge, was successful. These testing can report the actual stresses seen on the blades; detect synchronous resonances that are the source of high cycle fatigue(HCF) in blades; measure individual blade mis-tuning and coupled resonances in bladed disks. In order to minimize the error being created due to heat expansion, the tip timing sensor is installed parallel to the blade trailing edge, yielding optimal result. Also, when working on finite element analysis, the whole bladed disk has gone through three-dimensional analysis, evaluating the family mode. The result of the analysis matched well with the test result.

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Vibration Analysis of Bladed Disk using Non-contact Blade Vibration System (비접촉 진동측정 시스템을 이용한 블리스크의 진동분석)

  • Joung, Kyu-Kang;Kim, Myeong-Kuk;Park, Hee-Yong;Chen, Seung-Bae;Park, Noh-Gill
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.132-139
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    • 2008
  • The blade vibration problem of bladed disk is the most critical subject to consider since it directly affects the stable performance of the engine as well as life of the engine. Especially, due to complicated vibration pattern of the bladed disk, more effort was required for vibration analysis and test. The research of measuring the vibration of the bladed disk, using NSMS(Non-intrusive stress measurement) instead of Aeromechanics testing method requiring slip ring or telemetry system with strain gauge, was successful. These testing can report the actual stresses seen on the blades; detect synchronous resonances that are the source of high cycle fatigue (HCF) in blades; measure individual blade mis-tuning and coupled resonances in bladed disks. In order to minimize the error being created due to heat expansion, the tip timing sensor is installed parallel to the blade trailing edge, yielding optimal result. Also, when working on finite element analysis, the whole bladed disk has gone through three-dimensional analysis, evaluating the family mode. The result of the analysis matched well with the test result.

  • PDF