• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.827-833
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• 2017

In this paper, we define a set including of all $f_a$ with $a{\in}R$ generalized derivations of R and is denoted by $f_R$. It is proved that (i) the mapping $g:L(R){\rightarrow}f_R$ given by g (a) = f-a for all $a{\in}R$ is a Lie epimorphism with kernel $N_{{\sigma},{\tau}}$ ; (ii) if R is a semiprime ring and ${\sigma}$ is an epimorphism of R, the mapping $h:f_R{\rightarrow}I(R)$ given by $h(f_a)=i_{{\sigma}(-a)}$ is a Lie epimorphism with kernel $l(f_R)$ ; (iii) if $f_R$ is a prime Lie ring and A, B are Lie ideals of R, then $[f_A,f_B]=(0)$ implies that either $f_A=(0)$ or $f_B=(0)$.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.337-345
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• 2022

Let R ⊆ T be an extension of a commutative ring and S ⊆ R a multiplicative subset. We say that (R, T) is an S-accr (a commutative ring R is said to be S-accr if every ascending chain of residuals of the form (I : B) ⊆ (I : B²) ⊆ (I : B³) ⊆ ⋯ is S-stationary, where I is an ideal of R and B is a finitely generated ideal of R) pair if every ring A with R ⊆ A ⊆ T satisfies S-accr. Using this concept, we give an S-version of several different known results.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.319-329
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• 2017

Let I denote an ideal of a Noetherian local ring (R, m). Let M denote a finitely generated R-module. We study the endomorphism ring of the local cohomology module $H^c_I(M)$, c = grade(I, M). In particular there is a natural homomorphism $$Hom_{\hat{R}^I}({\hat{M}}^I,\;{\hat{M}}^I){\rightarrow}Hom_R(H^c_I(M),\;H^c_I(M))$$, $where{\hat{\cdot}}^I$ denotes the I-adic completion functor. We provide sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals $J{\subset}I$ with the property grade(I, M) = grade(J, M). Our results extends constructions known in the case of M = R (see e.g. [8], [17], [18]).

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.823-830
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• 2021

Let {R_i}_i∈I be an infinite family of rings and R = ∏_i∈I R_i their product. In this paper, we investigate the prime spectrum of R by 𝓕-limits. Special attention is paid to relationship between the elements of Spec(R_i) and the elements of Spec(∏_i∈I R_i) use 𝓕-lim, also we give a new condition so that ∏_i∈I R_i is a zero dimensional ring.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.17-29
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• 2022

A commutative ring with unity R is called an EM-ring if for any finitely generated ideal I there exist a in R and a finitely generated ideal J with Ann(J) = 0 and I = aJ. In this article it is proved that C(X) is an EM-ring if and only if for each U ∈ Coz (X), and each g ∈ C^* (U) there is V ∈ Coz (X) such that U ⊆ V, ${\bar{V}}=X$, and g is continuously extendable on V. Such a space is called an EM-space. It is shown that EM-spaces include a large class of spaces as F-spaces and cozero complemented spaces. It is proved among other results that X is an EM-space if and only if the Stone-Čech compactification of X is.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.1-8
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• 2002

We characterize the commutative Artinian rings R every proper quotient ring (respectively every proper ideal) in which is invariant with respect to all derivations.

• Journal of Power System Engineering
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• v.16 no.5
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• pp.63-69
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• 2012

This paper presents an analysis on the induction heating of ring flange for wind farm. Ring flange is used for the connection of poles when building a column of wind power plant. Heat treatment of ring flange with the diameter of ${\O}1,000mm$ has been considered. For analysis on the induction heating, FEA is used. Firstly, electromagnetic filed analysis was performed to get the induction current distribution on the steel, After that, heat transfer analysis was performed using the magnetic filed analysis results. for more precise analysis, some measurement for permeability has been performed and the measurement data was used during the analysis. From the analysis, we get the temperature distribution on the ring flange.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.415-427
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• 2019

Let R be an associative ring with nonzero identity. The annihilator ideal graph of R, denoted by ${\Gamma}_{Ann}(R)$, is a graph whose vertices are all nonzero proper left ideals and all nonzero proper right ideals of R, and two distinct vertices I and J are adjacent if $I{\cap}({\ell}_R(J){\cup}r_R(J)){\neq}0$ or $J{\cap}({\ell}_R(I){\cup}r_R(I)){\neq}0$, where ${\ell}_R(K)=\{b{\in}R|bK=0\}$ is the left annihilator of a nonempty subset $K{\subseteq}R$, and $r_R(K)=\{b{\in}R|Kb=0\}$ is the right annihilator of a nonempty subset $K{\subseteq}R$. In this paper, we assume that R is a semicommutative ring. We study the structure of ${\Gamma}_{Ann}(R)$. Also, we investigate the relations between the ring-theoretic properties of R and graph-theoretic properties of ${\Gamma}_{Ann}(R)$. Moreover, some combinatorial properties of ${\Gamma}_{Ann}(R)$, such as domination number and clique number, are studied.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.727-740
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• 2008

A ring R is called IFP, due to Bell, if ab=0 implies aRb=0 for $a,b{\in}R$. Huh et al. showed that the IFP condition need not be preserved by polynomial ring extensions. But it is shown that ${\sum}^n_{i=0}$ $E_{ai}E$ is a nonzero nilpotent ideal of E whenever R is an IFP ring and $0{\neq}f{\in}F$ is nilpotent, where E is a polynomial ring over R, F is a polynomial ring over E, and $a_i^{'s}$ are the coefficients of f. we shall use the term near IFP to denote such a ring as having place near at the IFPness. In the present note the structures of IFP rings and near-IFP rings are observed, extending the classes of them. IFP rings are NI (i.e., nilpotent elements form an ideal). It is shown that the near-IFPness and the NIness are distinct each other, and the relations among them and related conditions are examined.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1127-1133
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• 2014

Let S be a nonempty subset of a ring R. A map $f:R{\rightarrow}R$ is called strong commutativity preserving on S if [f(x), f(y)] = [x, y] for all $x,y{\in}S$, where the symbol [x, y] denotes xy - yx. Bell and Daif proved that if a derivation D of a semiprime ring R is strong commutativity preserving on a nonzero right ideal ${\rho}$ of R, then ${\rho}{\subseteq}Z$, the center of R. Also they proved that if an endomorphism T of a semiprime ring R is strong commutativity preserving on a nonzero two-sided ideal I of R and not identity on the ideal $I{\cup}T^{-1}(I)$, then R contains a nonzero central ideal. This short note shows that the conclusions of Bell and Daif are also true without the additivity of the derivation D and the endomorphism T.