• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.619-626
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• 2006

Let m be any positive integer, R be a ring with identity, $M_m(R)$ be the matrix ring of all m by m matrices eve. R and $G_m(R)$ be the multiplicative group of all n by n nonsingular matrices in $M_m(R)$. In this pape., the following are investigated: (1) for any pairwise coprime ideals ${I_1,\;I_2,\;...,\;I_n}$ in a ring R, $M_m(R/(I_1{\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $M_m(R/I_1){\times}M_m(R/I_2){\times}...{\times}M_m(R/I_n);$ and $G_m(R/I_1){\cap}I_2{\cap}...{\cap}I_n))$ is isomorphic to $G_m(R/I_1){\times}G_m(R/I_2){\times}...{\times}G_m(R/I_n);$ (2) In particular, if R is a finite ring with identity, then the order of $G_m(R)$ can be computed.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1167-1182
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• 2016

Let M be an R-module, where R is a commutative ring with identity 1 and let G(V,E) be a graph. In this paper, we study the graphs associated with modules over commutative rings. We associate three simple graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ to M called full annihilating, semi-annihilating and star-annihilating graph. When M is finite over R, we investigate metric dimensions in $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$. We show that M over R is finite if and only if the metric dimension of the graph $ann_f({\Gamma}(M_R))$ is finite. We further show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if M is a prime-multiplication-like R-module. We investigate the case when M is a free R-module, where R is an integral domain and show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if $$M{\sim_=}R$$. Finally, we characterize all the non-simple weakly virtually divisible modules M for which Ann(M) is a prime ideal and Soc(M) = 0.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.4
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• pp.569-573
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• 2010

We introduce the concept of fuzzy r-minimal preopen set on a fuzzy minimal space. We also introduce the concept of fuzzy r-M precontinuous mapping which is a generalization of fuzzy r-M continuous mapping, and investigate characterization of fuzzy r-M precontinuity.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.1
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• pp.128-131
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• 2011

In this paper, we introduce and study the concept of fuzzy r-$M^*$ preopen mappings between fuzzy r-minimal spaces. We also investigate the relationships among fuzzy r-M precontinuous mappings, fuzzy r-$M^*$-preopen mappings and several types of fuzzy r-minimal compactness.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.2
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• pp.250-253
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• 2011

In this paper, we study characterizations of fuzzy weakly r-M continuous function on r-minimal structures in terms of generalized fuzzy r-minimal open sets.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.141-148
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• 2010

We introduce the concept of fuzzy almost r-M continuous function on fuzzy r-minimal structures and investigate characterizations and properties for such a function.

• Journal of Korean Physical Therapy Science
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• v.8 no.2
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• pp.997-1003
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• 2001

The purpose of this study is to know the average of pint range of motion and difference according to the aging for the elderly, This study consisted of elder male(n=75) and elder female(n=l09), The result of assessment and analysis in shoulder pint range of motion are as follows: 1) The average shoulder flexion pint range of motion in 60-69(from sixty to sixty-nine)years old are 163.04(Left-Male), 162.91(Right-Male), 158.74 (Left-Female), 158.74 (Right-Female). 70-79years old are 149.40(L-M), 152.38(R-M), 153,37(L-F), 153.37(R-F). 80-89 years old are 149.57(L-M), 147.93(R-M), 151.17(L-F), 150.33(R-F). There was no significant difference among group, 2) The average shoulder extension pint range of motion in 60-69years old are 48.15(L-M), 47.20(R-M), 45.16(L-F), 44.23(R-F), 70-79years old are 37.l1(L-M), 38.70(R-M), 35.17(L-F), 36.71(R-F), 80-89 years old are 34.46(L-M). 36.71(R-M), 33.90(L-F), 33.09(R-F). There was significant difference among group(p<.05). 3) The average shoulder abduction pint range of motion in 60-69years old are 164.22(L-M), 165.96(R-M), 159.34(L-F), 159.97(R-F), 70-79years old are 152.27(L-M), 155.05(R-M), 152.32(L-F), 53.66(R-F), 80-89 years old are 152.17(L-M), 153.76(R-M), 147.53(L-F), 147.37(R-F). There was significant difference in right shoulder abduction among group(p<05). 4) The average shoulder internal rotation pint range of motion in 60-69years old are 63.52(L-M), 65.70(R-M), 64.16(L-F), 64.61(R-F), 70-79years old are 64.50(L-M), 65.81(R-M) 61.10(L-F), 61.83(R-F). 80-89 years old are 61.60(L-M), 61.66(R-M), 57.53(L-F), 57.53(R-F). There was no significant difference among group. 5) The average shoulder external rotation pint range of motion in 60-69years old are 50.87(L-M), 50.22(R-M), 51.03(L-F), 50.42(R-F), 70-79years old are 50.91(L-M), 50.20(R-M) 48.37(L-F), 50.20(R-F). 80-89 years old are 46.83(L-M), 47.93(R-M), 43.43(L-F), 43.72(R-F).There was significant difference in left shoulder external rotation among group(p<.05).

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.603-611
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• 2012

We introduce the concept of fuzzy $r$-minimal ${\alpha}$-open set on a fuzzy minimal space and some basic properties. We also introduce the concepts of fuzzy $r$-M ${\alpha}$-continuous and fuzzy $r$-M($M^*$) ${\alpha}$-open mappings, and investigate characterization for such mappings.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.163-165
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• 1994

Modules which satisfy the converse of Schur's lemma have been studied by many authors. In [6], R. Ware proved that a projective module P over a semiprime ring R is irreducible if and only if En $d_{R}$(P) is a division ring. Also, Y. Hirano and J.K. Park proved that a torsionless module M over a semiprime ring R is irreducible if and only if En $d_{R}$(M) is a division ring. In case R is a commutative ring, we obtain the following: An R-module M is irreducible if and only if En $d_{R}$(M) is a division ring and M is a multiplication R-module. Throughout this paper, R is commutative ring with identity and all modules are unital left R-modules. Let R be a commutative ring with identity and let M be an R-module. Then M is called a multiplication module if for each submodule N of M, there exists and ideal I of R such that N=IM. Cyclic R-modules are multiplication modules. In particular, irreducible R-modules are multiplication modules.dules.

• Journal of the korean academy of Pediatric Dentistry
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• v.8 no.1
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• pp.77-88
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• 1981

The purpose of this study was to make a comprehensive study & evaluation of the oral status of mental retarded children. The auther examined intraorally 486 (male; 311, female;175) mental retarded children. The result was as follows; (General mental retarded children means the children who live in their parent's home, & orphan mental retarded children means the children who live in orphanage.) 1. The dft rate was 31.6% in general mental retarded children (G.m.r.c.) & 20.7% in orphan mental retarded children (O. m. r. c.). The dft index was 3.73 in G.m.r.c. & 2.15 in O.m.r.c. 2. The DMFT rate was 24.6% in female G.m.r.c., 16.7% in male G.m.r.c., 12.7% in female O.m.r.c., 8.4% in male O.m.r.c. The DMFT index was 4.94 in female G.m.r.c., 4.01 in male G.m.r.c., 1.40 in male O.m.r.c., 2.75 in female O.m.r.c. 3. The malocclusion prevalence was 57.3%. the class I malocclusion was 14.2% Class II malocclusion 19.3%, Class III malocclusion 23.5%. The children with Down's syndrome had 60.0% of class III malocclusion prevalence. 4. The dental calculus index was 1.97 in male O.m.r.c., 1.81 in female O.m.r.c., 1.30 in male G.m.r.e., 1.13 in female G.m.r.c. 5. The dental plaque index was 3.06 in female G.m.r.c., 3.00 in male Gm.r.e. 2.70 in male O.m.r,c., 2.32 in female O.m.r.c.