• Title/Summary/Keyword: primary ideal

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ON 𝜙-n-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

  • Mostafanasab, Hojjat;Darani, Ahmad Yousefian
    • Journal of the Korean Mathematical Society
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    • v.53 no.3
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    • pp.549-582
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    • 2016
  • All rings are commutative with $1{\neq}0$ and n is a positive integer. Let ${\phi}:{\Im}(R){\rightarrow}{\Im}(R){\cup}\{{\emptyset}\}$ be a function where ${\Im}(R)$ denotes the set of all ideals of R. We say that a proper ideal I of R is ${\phi}$-n-absorbing primary if whenever $a_1,a_2,{\cdots},a_{n+1}{\in}R$ and $a_1,a_2,{\cdots},a_{n+1}{\in}I{\backslash}{\phi}(I)$, either $a_1,a_2,{\cdots},a_n{\in}I$ or the product of $a_{n+1}$ with (n-1) of $a_1,{\cdots},a_n$ is in $\sqrt{I}$. The aim of this paper is to investigate the concept of ${\phi}$-n-absorbing primary ideals.

SOME REMARKS ON THE PRIMARY IDEALS OF ℤpm[X]

  • Woo, Sung-Sik
    • Communications of the Korean Mathematical Society
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    • v.21 no.4
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    • pp.641-652
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    • 2006
  • In [2], they found some natural generators for the ideals of the finite ring $Z_{pm}$[X]/$(X^n\;-\;1)$, where p and n are relatively prime. If p and n are not relatively prime $X^n\;-\;1$ is not a product of basic irreducible polynomials but a product of primary polynomials. Due to this fact, to consider the ideals of $Z_{pm}$[X]/$(X^n\;-\;1)$ in 'inseparable' case we need to look at the primary ideals of $Z_{pm}$[X]. In this paper, we find a set of generators of ideals of $Z_{pm}$[X]/(f) for some primary polynomials f of $Z_{pm}$[X].

Detent Force Analysis in Permanent Magnet Linear Synchronous Motor Considering Longitudinal End Effects

  • Li, Liyi;Ma, Mingna;Chan, C.C.
    • Journal of international Conference on Electrical Machines and Systems
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    • v.2 no.1
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    • pp.9-15
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    • 2013
  • This paper presents a uniform analytical model by energy method and Fourier series expansion to analyze detent force in uneven magnetic field for permanent magnet linear synchronous motor (PMLSM). The model reveals that detent force in long-primary type is mainly influenced by non-ideal distribution of permanent magnet magnetic motive force, while nounified air-gap permeance makes a great impact on detent force of short-primary type. Hence, magnetic field similarity of motor design techniques referring rotary counterpart are adopted. For long-primary type novel method of splitting edge magnets is proposed to reduce end effects force, and optimal widths of edge tooth in short-primary type also verify the effectiveness of magnetic field similarity. The experimental results validate finite element analysis results.

Study on the Femininity and the Ideal Beauty of Body Implied in the fashion and the Anti-fashion Movement in the Victorian Period (I) (빅토리아시대 유행복식과 반(反)유행복식 운동에 나타난 여성성자 인체미에 관한 연구 (I))

  • 김정선;김민자
    • Journal of the Korean Society of Costume
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    • v.51 no.2
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    • pp.169-180
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    • 2001
  • This paper is intended to explore femininity, the ideal beauty of body and the features in fashion pursued in the fashion system and the Anti-Fashion Movement in the Victorian period, on which the modern fashion is based. For the informative facts needed in this paper, books on history, fashion history, feminism, art history of aestheticism and tole ideal beauty of body are referred to. On the part I of this paper, the femininity and the ideal beauty of body implied in the fashion system in the Victorian period will be reviewed. following are the conclusion : First, in the Victorian period, the value of femininity is put on the body of female by the discrimination of sex divided in two. Consequently, the characteristics of femininity mainly include dependence, passiveness, emotion, beauty, maternity, innocence, and purity. To emphasize the function of reproduction as primary duty and nature of female, the ideal beauty of body is represented in the form of Venus Naturalis, which symbolizes the fertility. And the external form of this body is expressed in slum waist line, ample busom and hip in fashion. Second, the features of this fashion are classified into three categories by their internal value : images of subordinate female, sensual female and maternal female 1) The image of subordinate female is expressed by concealment of legs, tightening the upper part of the body in corset and restriction on action by the crinoline 2) The image of sensual female is revealed in brazing colors and decoration, excessive exposure of the upper part of the body and hip by means of bustle. 3) The image of maternity is expressed in swollen skirt of crinoline, oval bustle silhouette metaphoring the extended womb resulted from pregnancy.

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PRIME FACTORIZATION OF IDEALS IN COMMUTATIVE RINGS, WITH A FOCUS ON KRULL RINGS

  • Gyu Whan Chang;Jun Seok Oh
    • Journal of the Korean Mathematical Society
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    • v.60 no.2
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    • pp.407-464
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    • 2023
  • Let R be a commutative ring with identity. The structure theorem says that R is a PIR (resp., UFR, general ZPI-ring, π-ring) if and only if R is a finite direct product of PIDs (resp., UFDs, Dedekind domains, π-domains) and special primary rings. All of these four types of integral domains are Krull domains, so motivated by the structure theorem, we study the prime factorization of ideals in a ring that is a finite direct product of Krull domains and special primary rings. Such a ring will be called a general Krull ring. It is known that Krull domains can be characterized by the star operations v or t as follows: An integral domain R is a Krull domain if and only if every nonzero proper principal ideal of R can be written as a finite v- or t-product of prime ideals. However, this is not true for general Krull rings. In this paper, we introduce a new star operation u on R, so that R is a general Krull ring if and only if every proper principal ideal of R can be written as a finite u-product of prime ideals. We also study several ring-theoretic properties of general Krull rings including Kaplansky-type theorem, Mori-Nagata theorem, Nagata rings, and Noetherian property.

ALMOST SPLITTING SETS S OF AN INTEGRAL DOMAIN D SUCH THAT DS IS A PID

  • Chang, Gyu Whan
    • Korean Journal of Mathematics
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    • v.19 no.2
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    • pp.163-169
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    • 2011
  • Let D be an integral domain, S be a multiplicative subset of D such that DS is a PID, and D[X] be the polynomial ring over D. We show that S is an almost splitting set in D if and only if every nonzero prime ideal of D disjoint from S contains a primary element. We use this result to give a simple proof of the known result that D is a UMT-domain and Cl(D[X]) is torsion if and only if each upper to zero in D[X] contains a primary element.

A Study on Classification of Obesity for Koreans based on the Articles in the Korean Journal of Community Nutrition - Articles Enlisted from 1996 to 2011 - (대한지역사회영양학회지 게재 논문에서의 한국인 비만 판정에 관한 연구 - 1996~2011년 게재 논문 분석 -)

  • Kim, Youngnam
    • Korean Journal of Community Nutrition
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    • v.18 no.5
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    • pp.525-538
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    • 2013
  • The purpose of this study was to provide information on obesity assessment for Koreans. Among total of 1012 research papers enlisted in the Korean J Community Nutrition form 1996 to 2011, 248 articles were examined in which subjects were divided into more than 2 groups by obesity rate. About the method of anthropometric data collection, more than half of the research papers examined 52.5% and 28.7% of studies utilized the directly measured data and self-described data, respectively. About the utilization of obesity assessment methods, indirect methods of weight-height index (BMI, BMI percentile, and R$\ddot{o}$hrer index) and PIBW (WLR, Broca index, and KDA) were 62.4% and 23.2%, respectably, and the direct method of percent body fat assessment was only 9.3%. The most frequently utilized methods were WLR in under primary and primary school children, and BMI in the middle and high school students and in adults. For primary school students, WLR was the most frequently utilized method up to 2007, but it changed to BMI percentile afterward. Broca Index was no longer utilized since 2008. There were no articles utilizing BMI percentile and R$\ddot{o}$hrer index for obesity assessment in adults. Criteria for obesity assessment were not consistent among research papers: for example, % body fat, 19~40%; BMI, 20~30; BMI percentile, 85th or 95th. In the case of PIBW, 120% of ideal weight was the most frequently utilized criterion for obesity. Based on these findings, we suggest that proper methods and criteria of obesity assessment for each age group should be determined and proclaimed.

Mother's perception for the importance of selected criteria of day care center according to the demographic characteristics (사회인구학적 변인에 따른 어머니의 보육시설 선택기준에 대한 중요도)

  • 안지연
    • Journal of the Korean housing association
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    • v.6 no.2
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    • pp.139-153
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    • 1995
  • The primary goals of this study were to find out how is the mother's perception for the importance of criteria when choosing day care center, and to examine how different there are according to the demographic characteristics, futhemore to investigate how different the importance of criteria when mothers choose an ideal day care center are given the present situation, when mother choose day care center are according to the related variables. The major results of this research are shown as follow: 1. Generally, there was significant differences in the mother's perception for the importance of quality criteria of day care center according to the demongraphic characteristics. 2. There were statistically significant differences in the importance of criteria when mothers choose day care center in 2 conditions: 1) given the present situation(income, trasportation, location of workplace etc.). when mothers choose day care center 2) when mothers choose an ideal day care center regardless of the present situation) according to several demographic variables.

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Improved Leakage Signal Blocking Methods for Two Channel Generalized Sidelobe Canceller

  • Kim, Ki-Hyeon;Ko, Han-Seok
    • Speech Sciences
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    • v.13 no.1
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    • pp.117-128
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    • 2006
  • The two-channel Generalized Sidelobe Canceller (GSC) scheme suffers from the presence of leakage signal in the reference channel. The leakage signal is caused by the dissimilar impulse responses between microphones, and different paths from speech source to microphones. Such leakage is detrimental to speech enhancement of the GSC since the desired reference signal becomes corrupted. In order to suppress the signal leakage, two matrix injection methods are proposed. In the first method, a simple gain compensation matrix is used. In the second, a projection matrix for reducing the error between the actual and the ideal primary and reference signals, is used. This paper describes the performance degradation resulting from leakage, and proposes effective methods to resolve the problem. Representative experiments were conducted to demonstrate the effectiveness of the proposed methods on recorded speech and noise in an actual automobile environment.

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ON STRONGLY QUASI J-IDEALS OF COMMUTATIVE RINGS

  • El Mehdi Bouba;Yassine EL-Khabchi;Mohammed Tamekkante
    • Communications of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.93-104
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    • 2024
  • Let R be a commutative ring with identity. In this paper, we introduce a new class of ideals called the class of strongly quasi J-ideals lying properly between the class of J-ideals and the class of quasi J-ideals. A proper ideal I of R is called a strongly quasi J-ideal if, whenever a, b ∈ R and ab ∈ I, then a2 ∈ I or b ∈ Jac(R). Firstly, we investigate some basic properties of strongly quasi J-ideals. Hence, we give the necessary and sufficient conditions for a ring R to contain a strongly quasi J-ideals. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the primary ideals, the prime ideals and the maximal ideals. Finally, we give an idea about some strongly quasi J-ideals of the quotient rings, the localization of rings, the polynomial rings and the trivial rings extensions.