• Title, Summary, Keyword: global dimension

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ON GORENSTEIN COTORSION DIMENSION OVER GF-CLOSED RINGS

  • Gao, Zenghui
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.173-187
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    • 2014
  • In this article, we introduce and study the Gorenstein cotorsion dimension of modules and rings. It is shown that this dimension has nice properties when the ring in question is left GF-closed. The relations between the Gorenstein cotorsion dimension and other homological dimensions are discussed. Finally, we give some new characterizations of weak Gorenstein global dimension of coherent rings in terms of Gorenstein cotorsion modules.

THE w-WEAK GLOBAL DIMENSION OF COMMUTATIVE RINGS

  • WANG, FANGGUI;QIAO, LEI
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.4
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    • pp.1327-1338
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    • 2015
  • In this paper, we introduce and study the w-weak global dimension w-w.gl.dim(R) of a commutative ring R. As an application, it is shown that an integral domain R is a $Pr\ddot{u}fer$ v-multiplication domain if and only if w-w.gl.dim(R) ${\leq}1$. We also show that there is a large class of domains in which Hilbert's syzygy Theorem for the w-weak global dimension does not hold. Namely, we prove that if R is an integral domain (but not a field) for which the polynomial ring R[x] is w-coherent, then w-w.gl.dim(R[x]) = w-w.gl.dim(R).

$\mathcal{F}_{\mathcal{S}}$-MITTAG-LEFFLER MODULES AND GLOBAL DIMENSION RELATIVE TO $\mathcal{F}_{\mathcal{S}}$-MITTAG-LEFFLER MODULES

  • Chen, Mingzhao;Wang, Fanggui
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.4
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    • pp.961-976
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    • 2019
  • Let R be any commutative ring and S be any multiplicative closed set. We introduce an S-version of $\mathcal{F}$-Mittag-Leffler modules, called $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and define the projective dimension with respect to these modules. We give some characterizations of $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, investigate the relationships between $\mathcal{F}$-Mittag-Leffler modules and $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and use these relations to describe noetherian rings and coherent rings, such as R is noetherian if and only if $R_S$ is noetherian and every $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler module is $\mathcal{F}$-Mittag-Leffler. Besides, we also investigate the $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension of R, and prove that $R_S$ is noetherian if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is zero; $R_S$ is coherent if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is at most one.

A Computer Aided Drawing Check System (Global Dimension Check) (컴퓨터 지원에 의한 설계도면 검증시스템)

  • ;Ono, T.;Tsujio, S.
    • 제어로봇시스템학회:학술대회논문집
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    • pp.1102-1107
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    • 1992
  • Existing CAD systems do nto provide the advanced function for systematic checking of design and drafting errors in mechanical drawings. This paper describes a method for sytematic checking of global parts in mechanical drawings. The checking items are deficiency and redundancy of dimensions, input-errors in dimension figures and symbols, etc. Checking for deficiency and redundancy of global dimensions has been performed applying Graph Theory. This system has been applied to several examples and we have confirmed the feasibility of this checing method.

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INJECTIVE COVERS OVER COMMUTATIVE NOETHERIAN RINGS WITH GLOBAL DIMENSION AT MOST TWO

  • Enochs, Edgar-E.;Kim, Hae-Sik;Song, Yeong-Moo
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.1
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    • pp.167-176
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    • 2003
  • In [3], Del Valle, Enochs and Martinez studied flat envelopes over rings and they showed that over rings as in the title these are very well behaved. If we replace flat with injective and envelope with the dual notion of a cover we then have the injective covers. In this article we show that these injective covers over the commutative noetherian rings with global dimension at most 2 have properties analogous to those of the flat envelopes over these rings.

The existence of a global solution for the nonlinear fuzzy differential equations in $E_N^{n_N}$ ($E_N^{n_N}$상의 비선형 퍼지 미분방정식에 대한 대역해의 존재성)

  • Kwun, Young-Chul;Kang, Jum-Ran;Park, Dong-Gun;Kim, Seon-Yu
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.1-4
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    • 2003
  • This paper we study the existence of a global solution for the nonlinear fuzzy differential equations in E$_{N}$$^{n}$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in R$^{n}$ . .

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GLOBAL ATTRACTORS FOR NONLOCAL PARABOLIC EQUATIONS WITH A NEW CLASS OF NONLINEARITIES

  • Anh, Cung The;Tinh, Le Tran;Toi, Vu Manh
    • Journal of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.531-551
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    • 2018
  • In this paper we consider a class of nonlocal parabolic equations in bounded domains with Dirichlet boundary conditions and a new class of nonlinearities. We first prove the existence and uniqueness of weak solutions by using the compactness method. Then we study the existence and fractal dimension estimates of the global attractor for the continuous semigroup generated by the problem. We also prove the existence of stationary solutions and give a sufficient condition for the uniqueness and global exponential stability of the stationary solution. The main novelty of the obtained results is that no restriction is imposed on the upper growth of the nonlinearities.

A Study on the Emotional Characteristics of Temporomandibular Disorder Patients using SCL-90-R (SCL-90-R을 이용한 측두하악장애 환자의 정서적 요인에 관한 연구)

  • Young-Ok Lee, DDS;ung-Woo Lee, DDS
    • Journal of Oral Medicine and Pain
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    • v.11 no.1
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    • pp.67-78
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    • 1986
  • This study was attempted to identify the emotional characteristics of temporomandibular disorder patients. The author applied one of the self-report modes of psychological measurement, Symptom Chechlist-90-Revision. The subjects were 219 TM disorder patients who visited the Department of Oral Diagnosis and Oral Medicine, Seoul National University Hospital during the period from December 1985 to September 1986. All the patients were divided into subgroup according sex, age, duration of symptoms, presence or absence of T-scores of each symptom dimension and global index. The obtained result were as follows : 1. Mean value of T-scores of each symptom dimension and global of the overall patients was within normal range. The two higher mean values of T-scores among 9 symptom dimensions were those of SOM and ANX. 2. Mean values of T-scores of females were higher than those of males in the O-C, DEP, ANX, HOS, PSY dimensions and all global indices, and there was a significant difference in the distribution of T-scores of the SOM dimension between males and female(P<0.05). 3. There was no significant difference between the subgroup under 30 years and the subgroup 30 years or older. 4. The subgroup with symptoms for 6 months or longer showed the higher mean values of T-scorers in the SOM, O-C, I-S, DEP, ANX, PHOB, PAR, PSY dimensions and all global indices compared with the subgroup with symptoms for shorter than 6 months. 5. The subgroup with pain showed the higher mean values of T-scores in all the symptom dimensions except the PAR in comparison with the subgroup with other complaints than pain, and there was a significant difference in the distribution of T-scores of the PST index between the pain subgroup and the non-pain subgroup(P<0.05). There was a significant difference in the distribution of T-scores of the PHOB dimension between the high-school graduates subgroup and the college graduates subgroup(P<0.05).

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