The Armendariz property on ideals

Kwak, Tai Keun,Lee, Yang,Yun, Sang Jo Elsevier 2012 Journal of algebra Vol.354 No.1

<P><B>Abstract</B></P><P>In the present note we study the Armendariz property on ideals of rings, introducing a new concept which unifies the Armendariz property and the insertion-of-factors-property (simply, IFP) for rings. In relation with this work, we investigate rings over which polynomial rings are IFP, called strongly IFP rings, which generalize both ideal-Armendariz rings and strongly reversible rings. The classes of minimal noncommutative ideal-Armendariz rings and strongly IFP rings, and the classes of minimal non-Abelian ideal-Armendariz rings and strongly IFP rings are completely determined, up to isomorphism. It is also shown that a local ring is Armendariz, symmetric, and strongly reversible (hence ideal-Armendariz) when the cardinality of the Jacobson radical is 4.</P>

On a ring property related to nilradicals

Hai Lan Jin,Zhelin Piao,윤상조 강원경기수학회 2019 한국수학논문집 Vol.27 No.1

In this article we investigate the structure of rings in which lower nilradicals coincide with upper nilradicals. Such rings shall be said to be quasi-2-primal. It is shown first that the K$\ddot{\text{o}}$the's conjecture holds for quasi-2-primal rings. So the results in this article may provide interesting and useful information to the study of nilradicals in various situations. In the procedure we study the structure of quasi-2-primal rings, and observe various kinds of quasi-2-primal rings which do roles in ring theory.

ON RADICALLY-SYMMETRIC IDEALS

Hashemi, Ebrahim Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.3

A ring R is called symmetric, if abc = 0 implies acb = 0 for a, b, c ${\in}$ R. An ideal I of a ring R is called symmetric (resp. radically-symmetric) if R=I (resp. R/$\sqrt{I}$) is a symmetric ring. We first show that symmetric ideals and ideals which have the insertion of factors property are radically-symmetric. We next show that if R is a semicommutative ring, then $T_n$(R) and R[x]=($x^n$) are radically-symmetric, where ($x^n$) is the ideal of R[x] generated by $x^n$. Also we give some examples of radically-symmetric ideals which are not symmetric. Connections between symmetric ideals of R and related ideals of some ring extensions are also shown. In particular we show that if R is a symmetric (or semicommutative) (${\alpha}$, ${\delta}$)-compatible ring, then R[x; ${\alpha}$, ${\delta}$] is a radically-symmetric ring. As a corollary we obtain a generalization of [13].

Inplane Vibration of Rotating Thin Ring Gyro with Thermoelastic Damping

Sun-Bae Kim,Young-Ho Na,Ji-Hwan Kim 한국항공우주학회 2008 한국항공우주학회 학술발표회 논문집 Vol.- No.-

For sensitive devices, such as resonant sensors, RF-MEMS filters. etc., high Quality factors (Q-factors) which mean the ratio of dissipation of total system energy occurred by various damping mechanism have been demanded. In this work. Q-factor for thermoelastic damping of the inplane vibration in rotating thin silicon rings is investigated. Especially, thermoelastic damping brings out the energy dissipation by irreversible heat flow of oscillating structures. Heat conduction equation for the thermal flow across the radial direction is solved to obtain the temperature profile in which bending approximation so-called in-extensional approximation is used. By using the preceding temperature profile coupled with displacement, governing equation of rotating thin rings can be acquired from Love's equations. Then, eigenvalue analysis is conducted to obtain the natural frequency of rotating thin rings. According to the definition of the Q-factors, finally, analytical form can be determined. Further, the effects of rotation. mode number, radius, radial thickness and axial depth on natural frequency and Q-factors are analyzed in detail.

On Isomorphism Theorems and Chinese Remainder Theorem in Hypernear Rings

M. Al Tahan,B. Davvaz 한국수학교육학회 2023 純粹 및 應用數學 Vol.30 No.4

The purpose of this paper is to consider the abstract theory of hypernear rings. In this regard, we derive the isomorphism theorems for hypernear rings as well as Chinese Remainder theorem. Our results can be considered as a generalization for the cases of Krasner hyperrings, near rings, and rings.

Notched Ring Test 저속균열 시험편의 응력확대계수정식화

표수호,최선웅,Pyo, Sooho,Choi, Sunwoong 한국재료학회 2014 한국재료학회지 Vol.24 No.2

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.

CRG 시스템의 접촉 피로수명

남형철(Hyoungchul Nam),김창현(Chang-Hyun Kim),권순만(Soon-Man Kwon) 대한기계학회 2012 대한기계학회 춘추학술대회 Vol.2012 No.5-3

Cam ring gear(CRG) system based on hypo trochoid curve consist of a pinion with roller teeth and its conjugated internal cam ring geear. In this paper, we investigated contact stress for surface pitting life using exact cam ring gear profile by introducing the profile modification factor to find characteristics of surface fatigue. Then, we present effective method to improve surface pitting life without any change of design parameters in CRG system. The results show that the pitting life can be extended significantly by increasing the profile modification factor.

물리적 보정된 핵의학 영상 평가 : 정규화 보정

박찬록,윤석환,이홍재,김진의,Park, Chan Rok,Yoon, Seok Hwan,Lee, Hong Jae,Kim, Jin Eui 대한핵의학기술학회 2017 핵의학 기술 Vol.21 No.1

QA 과정을 통해 30개의 정규화 보정값을 얻고, 1개의 기준 데이터 설정 후 29개의 정규화 보정값과 비교하였다. 또한 각 정규화 보정값을 PET raw data 에 적용시켜 재구성된 영상을 동일한 ROI를 그려 SUV 와 count 로 비교평가 하였다. 30개의 정규화 보정값은 차이가 발생하지 않았으며, 각각의 정규화 보정값을 적용시킨 PET 영상도 크게 차이가 없었다. 핵의학 영상은 정량분석을 위해 불감시간 보정 및 광자의 감쇠 및 산란 등 물리적 현상에 대한 보정이 필요하고, 정규화 보정 또한 무시할 수 없는 보정 과정이다. 따라서 이런 과정을 통해 PET 장비의 균일성이 유지되고 여러 디텍터의 효율도 균등해야 영상의 왜곡을 방지할 수 있고, 질 좋은 영상을 만드는데 꼭 필요한 과정이므로 매일 QA 과정이 필요하다고 사료된다. Purpose In this study, we evaluated image by applying normalization factor during 30 days to the PET images. Materials and Methods Normalization factor was acquired during 30 days. We compared with 30 normalization factors. We selected 3 clinical case (PNS study). We applied for normalization factor to PET raw data and evaluated SUV and count (kBq/ml) by drawing ROI to liver and lesion. Results There is no significant difference normalization factor. SUV and count are not different for PET image according to normalization factor. Conclusion We can get a lot of information doing the quality assurance such as performance of sinogram and detector. That's why we need to do quality assurance daily.

Outcome of Surgical Treatment of AO Type C Pelvic Ring Injury

( Do Hyeon Moon ),( Nam Ki Kim ),( Jun Sung Won ),( Jang Seok Choi ),( Dong Hyun Kim ) 대한고관절학회 2014 Hip and Pelvis Vol.26 No.4

Purpose: To evaluate the radiologic and clinical outcomes of AO type C pelvic ring injury and identify the prognostic factors. Materials and Methods: We studied 53 patients who were treated for AO type C pelvic ring injury from January 2002 to February 2010. Mean age and mean follow-up duration were 42.4 years and 14 months, respectively. We had 8 cases of AO type C1-1, 19 cases of C1-2, 11 cases of C1-3, 6 cases of C2 and 9 cases of C3 injury. We analyzed type of fracture, displacement, method of fixation and associated injuries. Radiologic outcome was evaluated with Matta and Saucedo criteria and clinical outcome was evaluated using Majeed score. Results: The average Majeed score was 86.2 distributing as 36 excellent cases, 15 good cases and 2 fair cases. Using radiologic Matta and Saucedo criteria, patients were divided as 31 excellent cases, 17 good cases and 5 fair cases. There was no significant difference between the outcomes of anterior, posterior and antero-posterior fixation. Neurologic injury was the reason for an unsatisfactory functional outcome. We identified two cases with complication, one with postoperative infection and the other with nonunion following anterior-posterior fixation. Conclusion: Satisfactory radiologic and clinical outcomes were obtained with open reduction and internal fixation in the management of AO type C pelvic ring injuries. Neurologic injuries affected the clinical outcome.

THE u-S-GLOBAL DIMENSIONS OF COMMUTATIVE RINGS

Wei Qi,Xiaolei Zhang 대한수학회 2023 대한수학회보 Vol.60 No.6

Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. First, we introduce and study the $u$-$S$-projective dimension and $u$-$S$-injective dimension of an $R$-module, and then explore the $u$-$S$-global dimension $u$-$S$-\gld$(R)$ of a commutative ring $R$, i.e., the supremum of $u$-$S$-projective dimensions of all $R$-modules. Finally, we investigate $u$-$S$-global dimensions of factor rings and polynomial rings.