• Kyungpook Mathematical Journal
• /
• v.50 no.1
• /
• pp.1-5
• /
• 2010

Let P be a prime ideal of a commutative unital ring R; X an indeterminate; D := R/P; L the quotient field of D; F an algebraic closure of L; ${\alpha}$ ${\in}$ L[X] a monic irreducible polynomial; ${\xi}$ any root of in F; and Q = ${\alpha}$>, the upper to P with respect to ${\alpha}$. Then R[X]/Q is R-algebra isomorphic to $D[{\xi}]$; and is R-isomorphic to an overring of D if and only if deg(${\alpha}$) = 1.

• East Asian mathematical journal
• /
• v.38 no.1
• /
• pp.1-12
• /
• 2022

Let R be a ring with an endomorphism σ and a σ-derivation δ. R is called (σ, δ)-Baer (resp. (σ, δ)-quasi-Baer, (σ, δ)-p.q.-Baer, (σ, δ)-p.p.) if the right annihilator of every right (σ, δ)-set (resp., (σ, δ)-ideal, principal (σ, δ)-ideal, (σ, δ)-element) of R is generated by an idempotent of R. In this paper, for a given Ore extension A = R[x; σ, δ] of R, the following properties are investigated: If R is a σ-rigid ring in which σ and δ commute, then (1) R is (σ, δ)-Baer if and only if R is (σ, δ)-quasi-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-quasi-Baer; (2) R is (σ, δ)-p.p. if and only if R is (σ, δ)-p.q.-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.p. if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.q.-Baer.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.529-545
• /
• 2022

This article concerns a ring property that arises from combining one-sided duo factor rings and centers. A ring R is called right CIFD if R/I is right duo by some proper ideal I of R such that I is contained in the center of R. We first see that this property is seated between right duo and right π-duo, and not left-right symmetric. We prove, for a right CIFD ring R, that W(R) coincides with the set of all nilpotent elements of R; that R/P is a right duo domain for every minimal prime ideal P of R; that R/W(R) is strongly right bounded; and that every prime ideal of R is maximal if and only if R/W(R) is strongly regular, where W(R) is the Wedderburn radical of R. It is also proved that a ring R is commutative if and only if D₃(R) is right CIFD, where D₃(R) is the ring of 3 by 3 upper triangular matrices over R whose diagonals are equal. Furthermore, we show that the right CIFD property does not pass to polynomial rings, and that the polynomial ring over a ring R is right CIFD if and only if R/I is commutative by a proper ideal I of R contained in the center of R.

• The Mathematical Education
• /
• v.12 no.2
• /
• pp.5-12
• /
• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• Journal of the Korean Dietetic Association
• /
• v.15 no.1
• /
• pp.1-9
• /
• 2009

The objective of this study was to assess the metabolic profiles and diet quality in college women by their mother's diabetes mellitus status. The study subjects, all college women, were classified into two groups based on the their mother's diabetes mellitus status: the offspring group (OG) and the control group (CG). The OG exhibited significantly higher body mass indices (p < 0.01), percentages of ideal body weight (p < 0.05) and high density lipoprotein cholesterol (p < 0.05) values than the CG. Additionally, the OG showed significantly higher daily average intakes of total energy (p < 0.05). fat (p < 0.001), riboflavin (p < 0.01) and calcium (0.01) than the CG. The indices of nutritional quality of protein (p < 0.05) and Na (p < 0.05) in the CG were significantly higher than those of the OG. However. we noted no significant differences in the mean adequacy ratio between the CG and OG. Overall, our results demonstrated that this factor appears to potentially be related to the subjects' mother's diabetes status. However, CG and OG were significantly different within normal range. Furthermore, nutrient adequacy indices in the CG were not assessed well in regard to energy, riboflavin, vitamin C, and calcium. Therefore, it appears that ideal body weight and diet quality should be controlled in order to prevent diabetes and diet-related problems, both in the CG and the OG.

• Korean Journal of Health Education and Promotion
• /
• v.21 no.3
• /
• pp.53-66
• /
• 2004

Purpose: To compare differences in BMI, body weight perception and satisfaction, and eating behavior by gender among middle school students. Methods: From 19 middle schools in W city four classes in two middle schools were selected by cluster sampling with multi-stage sampling. A structured questionnaire was answered by 143 adolescents. Results: Differences in BMI between boys and girls were significant (x$^2$=13.15, p=.00l). Boys reported higher ideal body weight than girls (t=6.33, p<.000l), and discrepancy between ideal body weight and body weight perception in girls was significantly greater than in boys(t=-5.0l, p<.0001). There was no significant gender difference in body weight perception but more boys were satisfied with their body weight(t=-4.48, p<.0001). Comparison of eating behavior showed that girls reported high scores in disinhibition (t=-2.29, p<.05) and hunger (t=-2.81, p<.01), while boys reported higher scores in cognitive restraints (t=3.22, p<.01). Conclusion: Interventions to help girls improve body image and satisfaction with body image are crucial. In order to establish proper diet habits and balanced nutritional status for adolescents, educational interventions should address characteristics of eating behaviors.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.3
• /
• pp.487-497
• /
• 2006

The purpose of this paper is to describe the structure of the rings $\mathbb{Z}_{p^2}[X]/({\alpha}(X))$ with ${\alpha}(X)$ a monic polynomial and $\={X}^{\kappa}=0$ for some nonnegative integer ${\kappa}$. Especially we will see that any ideal of such rings can be generated by at most two elements of the special form and we will find the 'minimal' set of generators of the ideals. We indicate how to identify the isomorphism types of the ideals as $\mathbb{Z}_{p^2}-modules$ by finding the isomorphism types of the ideals of some particular ring. Also we will find the annihilators of the ideals by finding the most 'economical' way of annihilating the generators of the ideal.

• Communications of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.359-370
• /
• 2022

The principal aim of this paper is to study the connection between the structure of a quotient ring R/P and the behavior of special additive mappings of R. More precisely, we characterize the commutativity of R/P using derivations (generalized derivations) of R satisfying algebraic identities involving the prime ideal P. Furthermore, we provide examples to show that the various restrictions imposed in the hypothesis of our theorems are not superfluous.

• Communications of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.365-376
• /
• 2023

The goal of this article is to present the graded J-ideals of G-graded rings which are extensions of J-ideals of commutative rings. A graded ideal P of a G-graded ring R is a graded J-ideal if whenever x, y ∈ h(R), if xy ∈ P and x ∉ J(R), then y ∈ P, where h(R) and J(R) denote the set of all homogeneous elements and the Jacobson radical of R, respectively. Several characterizations and properties with supporting examples of the concept of graded J-ideals of graded rings are investigated.

• Journal of applied mathematics & informatics
• /
• v.42 no.3
• /
• pp.539-548
• /
• 2024

Let R be a ring and P be a prime ideal of R. A mapping d : R → R is called a multiplicative derivation if d(xy) = d(x)y + xd(y) for all x, y ∈ R. In this paper, our main motive is to obtain the well-known theorem due to Posner in the ring R/P for generalized derivations associated with a multiplicative derivation defined by an additive mapping F : R → R such that F(xy) = F(x)y + xd(y), where d : R → R is a multiplicative derivation not necessarily additive. This article discusses the use of generalized derivations associated with a multiplicative derivation to investigate the commutativity of the quotient ring R/P.