• 대한수학회논문집
• /
• 제23권4호
• /
• pp.511-528
• /
• 2008

Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and $\upsilon$ be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple $\upsilon$-ideals $m\;=\;P_0\;{\supset}\;P_1\;{\supset}\;{\cdots}\;{\supset}\;P_t\;=\;P$ and all the other $\upsilon$-ideals are uniquely factored into a product of those simple ones [17]. Lipman further showed that the predecessor of the smallest simple $\upsilon$-ideal P is either simple or the product of two simple $\upsilon$-ideals. The simple integrally closed ideal P is said to be free for the former and satellite for the later. In this paper we describe the sequence of simple $\upsilon$-ideals when P is satellite of order 3 in terms of the invariant $b_{\upsilon}\;=\;|\upsilon(x)\;-\;\upsilon(y)|$, where $\upsilon$ is the prime divisor associated to P and m = (x, y). Denote $b_{\upsilon}$ by b and let b = 3k + 1 for k = 0, 1, 2. Let $n_i$ be the number of nonmaximal simple $\upsilon$-ideals of order i for i = 1, 2, 3. We show that the numbers $n_{\upsilon}$ = ($n_1$, $n_2$, $n_3$) = (${\lceil}\frac{b+1}{3}{\rceil}$, 1, 1) and that the rank of P is ${\lceil}\frac{b+7}{3}{\rceil}$ = k + 3. We then describe all the $\upsilon$-ideals from m to P as products of those simple $\upsilon$-ideals. In particular, we find the conductor ideal and the $\upsilon$-predecessor of the given ideal P in cases of b = 1, 2 and for b = 3k + 1, 3k + 2, 3k for $k\;{\geq}\;1$. We also find the value semigroup $\upsilon(R)$ of a satellite simple valuation ideal P of order 3 in terms of $b_{\upsilon}$.

• Korean Journal of Mathematics
• /
• 제7권2호
• /
• pp.215-218
• /
• 1999

We investigate characterizations of rings whose simple singular right R-modules are GP-injective. It is proved that if R is a semiprime ring whose simple singular right R-modules are GP-injective, then the center $Z(R)$ of R is a von Neumann regular ring. We consider the condition ($^*$): R satisfies $l(a){\subseteq}r(a)$ for any $a{\in}R$. Also it is shown that if R satisfies ($^*$) and every simple singular right R-module is GP-injective, then R is a reduced weakly regular ring.

• 대한수학회논문집
• /
• 제20권3호
• /
• pp.427-436
• /
• 2005

Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and v be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple v-ideals $m=P_0\;{\supset}\;P_1\;{\supset}\;{\cdotS}\;{\supset}\;P_t=P$ and all the other v-ideals are uniquely factored into a product of those simple ones. It then was also shown by Lipman that the predecessor of the smallest simple v-ideal P is either simple (P is free) or the product of two simple v-ideals (P is satellite), that the sequence of v-ideals between the maximal ideal and the smallest simple v-ideal P is saturated, and that the v-value of the maximal ideal is the m-adic order of P. Let m = (x, y) and denote the v-value difference |v(x) - v(y)| by $n_v$. In this paper, if the m-adic order of P is 2, we show that $O(P_i)\;=\;1\;for\;1\;{\leq}\;i\; {\leq}\;{\lceil}\;{\frac{b+1}{2}}{\rceil}\;and\;O(P_i)\;=2\;for\;{\lceil}\;\frac{b+3}{2}\rceil\;{\leq}\;i\;\leq\;t,\;where\;b=n_v$. We also show that $n_w\;=\;n_v$ when w is the prime divisor associated to a simple v-ideal $Q\;{\supset}\;P$ of order 2 and that w(R) = v(R) as well.

• 대한수학회논문집
• /
• 제19권4호
• /
• pp.601-618
• /
• 2004

Throughout this paper, we will consider that R is a near-ring and G an R-group. We initiate the study of monogenic, strongly monogenic R-groups, 3 types of nonzero R-groups and their basic properties. At first, we investigate some properties of D.G. (R, S)-groups, faithful R-groups, monogenic R-groups, simple and R-simple R-groups. Next, we introduce modular right ideals, t-modular right ideals and 3 types of primitive near-rings. The purpose of this paper is to investigate some properties of primitive types near-rings and their characterizations.

• Kyungpook Mathematical Journal
• /
• 제48권4호
• /
• pp.651-663
• /
• 2008

In this paper, we first study some characterizations of left MC2 rings. Next, by introducing left nil-injective modules, we discuss and generalize some well known results for a ring whose simple singular left modules are Y J-injective. Finally, as a byproduct of these results we are able to show that if R is a left MC2 left Goldie ring whose every simple singular left R-module is nil-injective and GJcp-injective, then R is a finite product of simple left Goldie rings.

• The Journal of Korean Physical Therapy
• /
• 제34권4호
• /
• pp.175-180
• /
• 2022

Purpose: Leg length discrepancy causes the posture deformation, gait asymmetry, and lower back pain. The purpose of this study is to investigate the correlation among functional leg length discrepancy (FLLD), muscle activity, muscle contraction onset time and vertical ground reaction force (vGRF) during simple lifting task. Methods: Thirty-nine subjects participated in this study. FLLD was measured from the umbilicus to medial malleolus of left and right leg using a tape. The subjects performed to lift a 10 kg box from the floor to chest. The muscle activity and muscle contraction onset time of rectus abdominis, erector spinae and rectus femoris was measured using EMG system and vGRF was measured by two force plate. Pearson correlation was used to fine out the correlation among FDDL, muscle activity, muscle contraction onset time and vGRF during simple lifting task. Results: Correlation between FLLD and difference of muscle activity of short-long side was very high (r>0.9) during simple lifting task. Correlation between FLLD and difference of muscle contraction onset time of short-long side was very high (r>0.9) during simple lifting task. And correlation between FLLD and difference of vGRF of short-long side was high (r>0.7) during simple lifting task. Conclusion: This study suggests that there is high correlation between FLLD and muscle activity, muscle contraction onset time, and ground reaction force during simple lifting task. Therefore, FLLD could negatively affect the postural balance.

• Fisheries and Aquatic Sciences
• /
• 제25권10호
• /
• pp.525-536
• /
• 2022

Photosynthetic bacteria (PSB) attract considerable interest as useful microorganisms; nevertheless, a generalized culture technique has not been previously reported owing to difficulty in their cultivation. Therefore, a simple culture technique suitable for public use was investigated. Among the PSB tested, the strain Rhodobacter azotoformans EBN-7 was the most suitable for scale-up production because it showed the highest specific growth rate (0.20 h^-1) on basal medium. In scale-up cultivation (500 L), R. azotoformans EBN-7 showed 4.50 × 10¹⁰ colony-forming units mL^-1 (number of viable cells), dry cell weight of 26.8 g/L, and a specific growth rate of 0.15 h^-1. Cultivation using this final culture broth (as seed culture) in a 15 L simple reactor was successful, with maintenance of cell activity evident. For use as seed culture, the maximum allowable preservation period of R. azotoformans EBN-7 at 4℃ was 3 months. When R. azotoformans EBN-7 cultivated in a simple technique was applied to shrimp aquaculture water, NH₄⁺-N was reduced from 0.61 mg/L to 0.24 mg/L (by 60.7%) in 4 days in comparison with the control. Thus, this simple culture technique using R. azotoformans EBN-7 has the potential for a good removal efficiency of NH₄⁺-N, making seed culture easier and suitable for public use.

• 대한수학회보
• /
• 제60권6호
• /
• pp.1687-1695
• /
• 2023

In this paper, we study the Green ring r(𝔴⁰_n) of the weak Hopf algebra 𝔴⁰_n based on Taft Hopf algebra H_n(q). Let R(𝔴⁰_n) := r(𝔴⁰_n) ⊗_ℤ ℂ be the Green algebra corresponding to the Green ring r(𝔴⁰_n). We first determine all finite dimensional simple modules of the Green algebra R(𝔴⁰_n), which is based on the observations of the roots of the generating relations associated with the Green ring r(𝔴⁰_n). Then we show that the nilpotent elements in r(𝔴⁰_n) can be written as a sum of finite dimensional indecomposable projective 𝔴⁰_n-modules. The Jacobson radical J(r(𝔴⁰_n)) of r(𝔴⁰_n) is a principal ideal, and its rank equals n - 1. Furthermore, we classify all finite dimensional non-simple indecomposable R(𝔴⁰_n)-modules. It turns out that R(𝔴⁰_n) has n² - n + 2 simple modules of dimension 1, and n non-simple indecomposable modules of dimension 2.

• East Asian mathematical journal
• /
• 제19권1호
• /
• pp.151-164
• /
• 2003

Throughout this paper, we will consider that R is a near-ring and G is an R-group. We initiate the study of monogenic and strongly monogenic R-groups and their basic properties. Also, we investigate some properties of D.G. R-groups, faithful R-groups and monogenic R-groups and we determine that when near-rings are rings.

• 대한수학회논문집
• /
• 제14권1호
• /
• pp.19-29
• /
• 1999

B. Gr nbaum defined the arrangements of simple curves and got many combinatorial properties. In this paper, we studied the existence of (n,r,t,k)-arrangements and the existence of digon-free(n,r,t,k)-arrangements, which is a generalized version of Gr nbaum`s definition.