• 대한수학회보
• /
• 제58권3호
• /
• pp.711-720
• /
• 2021

Let R denote a commutative noetherian ring, and let 𝐱 := x1, …, xd be an R-regular sequence. Suppose that 𝖆 denotes a monomial ideal with respect to 𝐱. The first purpose of this article is to show that 𝖆 is irreducible if and only if 𝖆 is a generalized-parametric ideal. Next, it is shown that, for any integer n ≥ 1, (x1, …, xd)n = ⋂P(f), where the intersection (irredundant) is taken over all monomials f = xe11 ⋯ xedd such that deg(f) = n - 1 and P(f) := (xe1+11, ⋯, xed+1d). The second main result of this paper shows that if 𝖖 := (𝐱) is a prime ideal of R which is contained in the Jacobson radical of R and R is 𝖖-adically complete, then 𝖆 is a parameter ideal if and only if 𝖆 is a monomial irreducible ideal and Rad(𝖆) = 𝖖. In addition, if a is generated by monomials m1, …, mr, then Rad(𝖆), the radical of a, is also monomial and Rad(𝖆) = (ω1, …, ωr), where ωi = rad(mi) for all i = 1, …, r.

• 대한수학회보
• /
• 제50권1호
• /
• pp.11-24
• /
• 2013

Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be ($m$, $n$)-injective if $Ext^1$(P, M) = 0 for any ($m$, $n$)-presented right R-module P; M is said to be ($m$, $n$)-flat if $Tor_1$(N, P) = 0 for any ($m$, $n$)-presented left R-module P. In terms of some derived functors, relative injective or relative flat resolutions and dimensions are investigated. As applications, some new characterizations of von Neumann regular rings and p.p. rings are given.

• 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 $b_{\upsilon}$.

• 대한기계학회논문집
• /
• 제17권5호
• /
• pp.1066-1073
• /
• 1993

Using regular finite elements and infinite elements simultaneously, elastic boundary value problems with infinite domain can be analyzed more effectively and accurately. In this paper, two dimensional infinite elements have been formulated by means of applying the derived mapping function to the coordinates and multiplying the regular displacement shape functions by a decay function. Orders(m, n) of the mapping and decay functions are found for the purpose of obtaining the convergent solutions without respect to the various decay lengthes. As a result of numerical tests for an infinite plate with a hole under internal pressure, two sets of function orders are obtained as follows. (a) n=0, m=1.5 (b) n=m=0.65

• 대한수학회보
• /
• 제59권5호
• /
• pp.1177-1190
• /
• 2022

Let R be a commutative ring with identity. We call the ring R to be an almost quasi-coherent ring if for any finite set of elements α₁, …, α_p and a of R, there exists a positive integer m such that the ideals $\bigcap{_{i=1}^{p}}\;R{\alpha}^m_i$ and Ann_R(α^m) are finitely generated, and to be almost von Neumann regular rings if for any two elements a and b in R, there exists a positive integer n such that the ideal (αⁿ, bⁿ) is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.

• 대한수학회지
• /
• 제49권5호
• /
• pp.1031-1051
• /
• 2012

In this paper, we will investigate the concept of the torsion-graph of an R-module M, in which the set $T(M)^*$ makes up the vertices of the corresponding torsion graph, ${\Gamma}(M)$, with any two distinct vertices forming an edge if $[x:M][y:M]M=0$. We prove that, if ${\Gamma}(M)$ contains a cycle, then $gr({\Gamma}(M)){\leq}4$ and ${\Gamma}(M)$ has a connected induced subgraph ${\overline{\Gamma}}(M)$ with vertex set $\{m{\in}T(M)^*{\mid}Ann(m)M{\neq}0\}$ and diam$({\overline{\Gamma}}(M)){\leq}3$. Moreover, if M is a multiplication R-module, then ${\overline{\Gamma}}(M)$ is a maximal connected subgraph of ${\Gamma}(M)$. Also ${\overline{\Gamma}}(M)$ and ${\overline{\Gamma}}(S^{-1}M)$ are isomorphic graphs, where $S=R{\backslash}Z(M)$. Furthermore, we show that, if ${\overline{\Gamma}}(M)$ is uniquely complemented, then $S^{-1}M$ is a von Neumann regular module or ${\overline{\Gamma}}(M)$ is a star graph.

• 복식
• /
• 제53권6호
• /
• pp.145-159
• /
• 2003

The purpose of this study was to classify body type for ready-to-wear sizes. The subjects were 300 women ages of 18-24. they were measured direct anthropometry. The body types for sizing system were divided by Rohrer Index. KS drop value and ISO drop value. The results of this study were as follows. 1. By adapting the Rohrer Index. we classify 3 types from anthropometric measurements. The thin type covered 39.3%, the standard type 51.0% and the obesity type 18.7%. The characteristics of clusters were as follows. Thin type was characterized by tall. slender type and slim. The standard type was characterized by middle sized. The obesity type was characterized by short. fat type. and large bust. 2. By adapting the KS system drop value. we classify 3 types from anthropometric measurements. The H type(drop 0) covered 25.6%. the N type(drop 6) 65.2% and the A type(drop 12) 9.2%. Type H was slightly tall large bust. and curved from waist to hip. Type A was slightly thin. large hip and smaller bust than type N. Principal factor components were bust size. The height could be divided into three groups. The Petite(l50cm) covered 5.5%. the Regular(l60cm) 64.7% and the Tall(l70cm) 29.8%. Through the crosstab of height and body type. we extracted regular height by N type 46.2% the largest cell. The body type was the higher order of N type. H type and A type. The tall was the higher order of Regular. Tall and Petite. 3. By adapting the ISO system drop value. we classify 3 types from anthropometric measurements. The H type(drop 0) covered 15.0%. the M type(drop 6) 41.0% and the A type(drop 12) 44.0%. Type H was slightly short. slightly fat and large bust. Type A was slightly tall. slight thin than type M. The height could be divided into three groups. We adjust the height section after allow for height distribution. The Short(152cm) covered 12.8%. the Regular(160cm) 66.9% and the Long(168cm) 20.3%. Through the crosstab of height and body type, we extracted regular height by M type 29.3% the largest cell. The body type was the higher order of M type, A type and H type. The tall was the higher order of Regular, Long and short.

• 충청수학회지
• /
• 제15권2호
• /
• pp.41-46
• /
• 2003

In this paper, we investigate the $SP_{\alpha}$-integral and the $M_{\alpha}$-integral defined on an interval of the n-dimensional Euclidean space $\mathbb{R}^n$. In particular, we show that these two integrals are equivalent.

• Journal of applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.351-360
• /
• 2005

Let T be a regular semigroup and let S be a regular subsemigroup of T. In this paper we study the relationship between the idempotent separating congruence on S and the idempotent separating congruence on T, when T and S are connected by a splitmap ${\theta} : T {\to} S$.

• 생명과학회지
• /
• 제21권7호
• /
• pp.997-1003
• /
• 2011

폐경과 비만은 여러 대사증후군과 관련되어 있다. 이에 본 연구는 난소절제로 폐경을 유도한 흰쥐에게 고지방식이로 비만을 유도하여 이들 지방세포에서 발현되는 PPAR${\gamma}$, PGC-$1{\alpha}$, -$1{\beta}$, NRf-1, TFAM 유전자들의 변화를 조사하고 6주간의 규칙적인 운동을 하여 그 차이에 따른 효과를 규명하는데 목적을 두고 조사하였다. 본 실험에서 사용한 암컷흰쥐는 3그룹으로 다음과 같이 구분하였다. (1) 일반식이군(C group, n=4), (2) 고지방식이 군(H group, n=4), (3) 고지방식이와 운동군(H+EX group, n=4)으로 나누었다. 규칙적인 운동은 수영운동을 하였으며, 방법은 주 5회, 총 6주간 점진적 시간증가로 수행하였다. 그 결과, 지방조직의 무게는 H 그룹에서 유의하게 높게 (p<0.01) 나타났으나 규칙적인 운동그룹은 확실히 감소되었다. 또한 규칙적인 운동은 PPAR-${\gamma}$ (p<0.05), PGC-$1{\alpha}$ (p<0.01), -$1{\beta}$ (p<0.05), NRf-1 (p<0.01), TFAM (p<0.05)의 유전자들은 모두 유의하게 증가시켰다. 이상의 결과를 종합하면 6주간의 규칙적인 수영운동은 지방세포 내 PPAR-${\gamma}$, PGC-$1{\alpha}$, -$1{\beta}$, NRf-1, TFAM의 mRNA 발현 증가와 미토콘드리아의 수 증가에 영향을 미친 것으로 추측된다. 따라서 규칙적인 운동은 폐경기 비만으로 비대해진 피하지방을 감소시키고 지방세포 내 미토콘드리아의 생합성기능을 개선시켜 미토콘드리아 수 감소를 개선할 수 있을 것으로 생각된다.