• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.65-72
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• 2014

A ring R is called weakly semicommutative ring if for any a, $b{\in}R^*$ = R\{0} with ab = 0, there exists $n{\geq}1$ such that either an $a^n{\neq}0$ and $a^nRb=0$ or $b^n{\neq}0$ and $aRb^n=0$. In this paper, many properties of weakly semicommutative rings are introduced, some known results are extended. Especially, we show that a ring R is a strongly regular ring if and only if R is a left SF-ring and weakly semicommutative ring.

• East Asian mathematical journal
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• 제1권
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• pp.89-100
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• 1985

A mapping f: X$\rightarrow$Y is introduced to be weakly irresolute if, for each x $\varepsilon$ X and each semi-neighborhood V of f(x), there exists a semi-neighborhood U of x in X such that $f(U){\subset}scl(V)$. It will be shown that a mapping f: X$\rightarrow$Y is weakly irresolute iff(if and only if) $f^{-1}(V){\subset}sint(f^{_1}(scl(V)))$ for each semiopen subset V of Y. The relationship between mappings described in [3,5, 6,8] and a weakly irresolute mapping. will be investigated and it will be shown that every irresolute retract of a $T_2$-space is semiclosed.

• 대한수학회보
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• 제28권2호
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• pp.175-180
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• 1991

In [3], [4] and [5], Hochster and Huneke introduced the notions of the tight closure of an ideal and of the weak F-regularity of a ring. This notion enabled us to give new proofs of many results in commutative algebra. A regular ring is known to be F-regular, and a Gorenstein local ring is proved to be F-regular provided that one ideal generated by a system of parameters (briefly s.o.p.) is tightly closed. In fact, a Gorenstein local ring is weakly F-regular if and only if there exists a system of parameters ideal which is tightly closed [3]. But we do not know whether this fact is true or not if a ring is not Gorenstein, in particular, a ring is a Cohen Macaulay (briefly C-M) local ring. In this paper, we will prove this in the case of an 1-dimensional C-M local ring. For this, we study the F-rationality and the normality of the ring. And we will also prove that a C-M local ring is to be Gorenstein under some additional condition about the tight closure.

• 대한수학회논문집
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• 제38권1호
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• pp.11-19
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• 2023

Let 𝓗₀ be the set of rings R such that Nil(R) = Z(R) is a divided prime ideal of R. The concept of maximal non φ-chained subrings is a generalization of maximal non valuation subrings from domains to rings in 𝓗₀. This generalization was introduced in [20] where the authors proved that if R ∈ 𝓗₀ is an integrally closed ring with finite Krull dimension, then R is a maximal non φ-chained subring of T(R) if and only if R is not local and |[R, T(R)]| = dim(R) + 3. This motivates us to investigate the other natural numbers n for which R is a maximal non φ-chained subring of some overring S. The existence of such an overring S of R is shown for 3 ≤ n ≤ 6, and no such overring exists for n = 7.

• 대한수학회논문집
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• 제31권2호
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• pp.229-235
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• 2016

In this paper we study the regularity of inside (or outside) (${\theta},{\phi}$)-derivations in BCI-algebras X and prove that let $d_{({\theta},{\phi})}:X{\rightarrow}X$ be an inside (${\theta},{\phi}$)-derivation of X. If there exists a ${\alpha}{\in}X$ such that $d_{({\theta},{\phi})}(x){\ast}{\theta}(a)=0$, then $d_{({\theta},{\phi})}$ is regular for all $x{\in}X$. It is also shown that if X is a BCK-algebra, then every inside (or outside) (${\theta},{\phi}$)-derivation of X is regular. Furthermore the concepts of ${\theta}$-ideal, ${\phi}$-ideal and invariant inside (or outside) (${\theta},{\phi}$)-derivations of X are introduced and their related properties are investigated. Finally we obtain the following result: If $d_{({\theta},{\phi})}:X{\rightarrow}X$ is an outside (${\theta},{\phi}$)-derivation of X, then $d_{({\theta},{\phi})}$ is regular if and only if every ${\theta}$-ideal of X is $d_{({\theta},{\phi})}$-invariant.

• 대한수학회보
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• 제29권1호
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• pp.65-72
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• 1992

All rings are commutative, Noetherian with identity and of prime characteristic p, unless otherwise specified. First, we describe the definition of tight closure of an ideal and the properties about the tight closure used frequently. The technique used here for the tight closure was introduced by M. Hochster and C. Huneke [4,5, or 6]. Using the concepts of the tight closure and its properties, we will prove that if R is a complete local domain and F-rational, then R is Cohen-Macaulay. Next, we study the properties of R$^{+}$, the integral closure of a domain in an algebraic closure of its field of fractions. In fact, if R is a complete local domain of characteristic p>0, then R$^{+}$ is Cohen-Macaulay [8]. But we do not know this fact is true or not if the characteristic of R is zero. For the special case we can show that if R is a non-Cohen-Macaulay normal domain containing the rationals Q, then R$^{+}$ is not Cohen-Macaulay. Finally we will prove that if R is an excellent local domain of characteristic p and F-ratiional, then R is Cohen-Macaulay.aulay.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.289-300
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• 2015

In [9], the author extends the definition of lifting and supplemented modules to ${\delta}$-lifting and ${\delta}$-supplemented by replacing "small submodule" with "${\delta}$-small submodule" introduced by Zhou in [13]. The aim of this paper is to show new properties of ${\delta}$-lifting and ${\delta}$-supplemented modules. Especially, we show that any finite direct sum of ${\delta}$-hollow modules is ${\delta}$-supplemented. On the other hand, the notion of amply ${\delta}$-supplemented modules is studied as a generalization of amply supplemented modules and several properties of these modules are given. We also prove that a module M is Artinian if and only if M is amply ${\delta}$-supplemented and satisfies Descending Chain Condition (DCC) on ${\delta}$-supplemented modules and on ${\delta}$-small submodules. Finally, we obtain the following result: a ring R is right Artinian if and only if R is a ${\delta}$-semiperfect ring which satisfies DCC on ${\delta}$-small right ideals of R.

• 대한수학회지
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• 제60권6호
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• pp.1233-1254
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• 2023

We introduce two subclasses of abelian McCoy rings, so-called π-CN-rings and π-duo rings, and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as 2-primal rings, bounded rings etc. It is shown that a ring R is π-CN whenever every nilpotent element of index 2 in R is central. These rings naturally generalize the long-known class of CN-rings, introduced by Drazin [9]. It is proved that π-CN-rings are abelian, McCoy and 2-primal. We also show that, π-duo rings are strongly McCoy and abelian and also they are strongly right AB. If R is π-duo, then R[x] has property (A). If R is π-duo and it is either right weakly continuous or every prime ideal of R is maximal, then R has property (A). A π-duo ring R is left perfect if and only if R contains no infinite set of orthogonal idempotents and every left R-module has a maximal submodule. Our achieved results substantially improve many existing results.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제4권3호
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• pp.428-451
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• 2010

Traffic matrix-based anomaly detection and DDoS attacks detection in networks are research focus in the network security and traffic measurement community. In this paper, firstly, a new type of unidirectional flow called IF flow is proposed. Merits and features of IF flows are analyzed in detail and then two efficient methods are introduced in our DDoS attacks detection and evaluation scheme. The first method uses residual variance ratio to detect DDoS attacks after Recursive Least Square (RLS) filter is applied to predict IF flows. The second method uses generalized likelihood ratio (GLR) statistical test to detect DDoS attacks after a Kalman filter is applied to estimate IF flows. Based on the two complementary methods, an evaluation formula is proposed to assess the seriousness of current DDoS attacks on router ports. Furthermore, the sensitivity of three types of traffic (IF flow, input link and output link) to DDoS attacks is analyzed and compared. Experiments show that IF flow has more power to expose anomaly than the other two types of traffic. Finally, two proposed methods are compared in terms of detection rate, processing speed, etc., and also compared in detail with Principal Component Analysis (PCA) and Cumulative Sum (CUSUM) methods. The results demonstrate that adaptive filter methods have higher detection rate, lower false alarm rate and smaller detection lag time.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2003년도 추계학술대회 논문집(II)
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• pp.58-63
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• 2003

This study shows the functional contribution into the public transportation system for congestion area. And there is a introduction for the rapid bus transit developed in Europe community. It can be classified the public transportation as urban transit, subway and bus. For a few years, it has been introduced the AGT system as a role of the alternative and lengthening system of subway line. Recently, there is going on construction of AGT system in some regional cities. The AGT system has advantages in terms of accessibility and cost-effective rather than subway. But the bus system is advantageous at the points rather than AGT system. It is obvious that the bus system is most cost-effective for infrastructure and system rather than any other public transports. If the bus system has punctuality and precise docking, that becomes best choice for public transportation scheme. There are tries to develop new systems by means of the f1les up the advantages in bus and AGT system, which can be classified as BRT(Bus Rapid Transit}. The idea is simple; 'Thirik rail, use advanced buses.' It is introduced the IRISBUS system at this article, which was developed in Europe community. And it is introduced the project architecture to develop the similar system to IRISBUS in KRRI through National Transportation Key Technology R&D Project