• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.861-866
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• 2016

A ring R called left SF if its simple left modules are at. Regular rings are known to be left SF-rings. However, till date it is unknown whether a left SF-ring is necessarily regular. In this paper, we prove the strong regularity of left (right) complement bounded left SF-rings. We also prove the strong regularity of a class of generalized semi-commutative left SF-rings.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.53-58
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• 1994

In this note, we study conditions under which SF-rings are semi-simple. We prove that left SF-rings are semisimple for each of the following classes of rings: (1) left non-singular rings of finite rank; (2) rings whose maximal left ideals are finitely generated; (3) rings of pure global dimension zero and (4) rings which is pure-split. Also it is shown that left SF-rings without zero-divisors are semisimple.

• Kyungpook Mathematical Journal
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• v.53 no.3
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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.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.1
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• pp.39.1-39.1
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• 2012

Nuclear rings in barred galaxies are sites of active star formation (SF). We investigate SF and its feedback effects occurring in barred galaxies, for the first time, using high-resolution grid-based hydrodynamic simulations. The gaseous medium is assumed to be infinitesimally thin, isothermal, and unmagnetized. The SF recipes include a density threshold corresponding to the Jeans condition, a SF efficiency of 1%, and momentum feedback via Type II supernova events together with stellar-wind mass loss. To investigate various environments, we vary the gas sound speed as well as the efficiency of momentum injection in the in-plane direction. We find that when the sound speed is small, the surface density of a ring becomes largely independent of the azimuthal angle, resulting in star-forming regions distributed over the whole length of the ring. When the sound speed is large, on the other hand, the ring achieves the largest density at the contact points between the dust lanes and the ring where SF occurs preferentially, leading to a clear age gradient of star clusters in the azimuthal direction. Since rings shrink with time, a radial age gradient of star clusters naturally develop regardless of sound speed, consistent with observations. SF persists over 200 Myr, with an average rate of ${\sim}1.3M_{\odot}/yr$ similar to observed values. Rings gradually become hostile to SF as they lose gas into stars and turbulent motions dominate.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.65-72
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• 2014

A ring R is called weakly semicommutative ring if for any a, $b{\in}R^*$ = R\{0} with ab = 0, there exists $n{\geq}1$ such that either an $a^n{\neq}0$ and $a^nRb=0$ or $b^n{\neq}0$ and $aRb^n=0$. In this paper, many properties of weakly semicommutative rings are introduced, some known results are extended. Especially, we show that a ring R is a strongly regular ring if and only if R is a left SF-ring and weakly semicommutative ring.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1381-1388
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• 2018

Let ${\Delta}$ be a simplicial complex, $I_{\Delta}$ its Stanley-Reisner ideal and $K[{\Delta}]$ its Stanley-Reisner ring over a field K. Assume that ${\Gamma}(R)$ denotes the zero-divisor graph of a commutative ring R. Here, first we present a condition on two reduced Noetherian rings R and R', equivalent to ${\Gamma}(R){\cong}{\Gamma}(R{^{\prime}})$. In particular, we show that ${\Gamma}(K[{\Delta}]){\cong}{\Gamma}(K^{\prime}[{\Delta}^{\prime}])$ if and only if ${\mid}Ass(I_{\Delta}){\mid}={\mid}Ass(I_{{{\Delta}^{\prime}}}){\mid}$ and either ${\mid}K{\mid}$, ${\mid}K^{\prime}{\mid}{\leq}{\aleph}_0$ or ${\mid}K{\mid}={\mid}K^{\prime}{\mid}$. This shows that ${\Gamma}(K[{\Delta}])$ contains little information about $K[{\Delta}]$. Then, we define the squarefree zero-divisor graph of $K[{\Delta}]$, denoted by ${\Gamma}_{sf}(K[{\Delta}])$, and prove that ${\Gamma}_{sf}(K[{\Delta}){\cong}{\Gamma}_{sf}(K[{\Delta}^{\prime}])$ if and only if $K[{\Delta}]{\cong}K[{\Delta}^{\prime}]$. Moreover, we show how to find dim $K[{\Delta}]$ and ${\mid}Ass(K[{\Delta}]){\mid}$ from ${\Gamma}_{sf}(K[{\Delta}])$.

• Journal of the Semiconductor & Display Technology
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• v.22 no.4
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• pp.7-12
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• 2023

The edge ring placed on the outside of the electrostatic chuck (ESC) is a key component for protecting the ESC and controlling the etching uniformity of the edge of the wafer. Therefore, it is very important to understand the etching phenomenon of edge rings for edge ring management and equipment homeostasis. In this study, a specimen with SiO₂ hard mask and underlying Si mold was installed on the edge ring surface and the etching results were measured by varying the edge ring 2MHz RF power. By developing PI-VM model with high prediction accuracy and analyzing the roles of key parameters in the model, we were able to evaluate the effect of plasma and sheath characteristics around the edge ring on edge ring erosion. This analysis method provided information necessary for edge ring maintenance and operation.

• International Journal of Oral Biology
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• v.45 no.1
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• pp.15-24
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• 2020

The fruit of Chaenomeles sinensis (Thouin) Koehne (Chaenomelis Fructus) known as "Mo-Gua" in Korea has been commonly used in traditional medicine to treat inflammatory diseases, such as sore throat. However, its effect on bone metabolism has not been elucidated yet. Here, we examined the effect of Chaenomelis Fructus ethanol extract (CF-E) on receptor activator of nuclear factor (NF)-κB ligand (RANKL)-mediated osteoclast differentiation and formation. CF-E considerably inhibited osteoclast differentiation and tartrate-resistant acid phosphatase-positive multinuclear cell formation from bone marrow-derived macrophages and osteoclast precursor cells in a dose-dependent manner. In addition, the formation of actin rings and resorption pits were significantly suppressed in CF-E-treated osteoclasts as compared with the findings in non-treated control cells. Consistent with these phenotypic inhibitory results, the expressions of osteoclast differentiation marker genes (Acp5, Atp6v0d2, Oscar, CtsK, and Tm7sf4) and Nfatc1, a pivotal transcription factor for osteoclastogenesis, were markedly decreased by CF-E treatment. The inhibitory effect of CF-E on RANKL-induced osteoclastogenesis was associated with the suppression of NFATc1 expression, not by regulation of mitogen-activated protein kinases and NF-κB activation but by the inactivation of phospholipase C gamma 1 and 2. These results indicate that CF-E has an inhibitory effect on osteoclast differentiation and formation, and they suggest the possibility of CF-E as a traditional therapeutic agent against bone-resorptive diseases, such as osteoporosis, rheumatoid arthritis, and periodontitis.