• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.489-496
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• 2012

In this paper, we introduce the notions of Smarandache weak BE-algebra, Q-Smarandache filters and Q-Smarandache ideals. We show that a nonempty subset F of a BE-algebra X is a Q-Smarandache filter if and only if $A(x,y){\subseteq}F$, which A($x,y$) is a Q-Smarandache upper set The relationship between these notions are stated and proved.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.455-466
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• 2010

For an endomorphism $\alpha$ of a ring R, we introduce the weak $\alpha$-skew Armendariz rings which are a generalization of the $\alpha$-skew Armendariz rings and the weak Armendariz rings, and investigate their properties. Moreover, we prove that a ring R is weak $\alpha$-skew Armendariz if and only if for any n, the $n\;{\times}\;n$ upper triangular matrix ring $T_n(R)$ is weak $\bar{\alpha}$-skew Armendariz, where $\bar{\alpha}\;:\;T_n(R)\;{\rightarrow}\;T_n(R)$ is an extension of $\alpha$ If R is reversible and $\alpha$ satisfies the condition that ab = 0 implies $a{\alpha}(b)=0$ for any a, b $\in$ R, then the ring R[x]/($x^n$) is weak $\bar{\alpha}$-skew Armendariz, where ($x^n$) is an ideal generated by $x^n$, n is a positive integer and $\bar{\alpha}\;:\;R[x]/(x^n)\;{\rightarrow}\;R[x]/(x^n)$ is an extension of $\alpha$. If $\alpha$ also satisfies the condition that ${\alpha}^t\;=\;1$ for some positive integer t, the ring R[x] (resp, R[x; $\alpha$) is weak $\bar{\alpha}$-skew (resp, weak) Armendariz, where $\bar{\alpha}\;:\;R[x]\;{\rightarrow}\;R[x]$ is an extension of $\alpha$.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.333-344
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• 2023

In this paper, we generalize the notions uniformly S-flat, briefly u-S-flat, modules and dimensions. We introduce and study the notions of weak u-S-flat modules. An R-module M is said to be weak u-S-flat if Tor^R₁ (R/I, M) is u-S-torsion for any ideal I of R. This new class of modules will be used to characterize u-S-von Neumann regular rings. Hence, we introduce the weak u-S-flat dimensions of modules and rings. The relations between the introduced dimensions and other (classical) homological dimensions are discussed.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.303-303
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• 2019

• Communications of the Korean Mathematical Society
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• v.23 no.1
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• pp.1-10
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• 2008

Conditions for an ideal to be irreducible are provided. The notion of an order system in a subtraction algebra is introduced, and related properties are investigated. Relations between ideals and order systems are given. The concept of a fixed map in a subtraction algebra is discussed, and related properties are investigated.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1855-1861
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• 2013

Let R be a commutative Noetherian ring, I an ideal of R, M and N two R-modules. We characterize the least integer i such that $H^i_I(M,N)$ is not weakly Artinian by using the notion of weakly filter regular sequences. Also, a local-global principle for minimax generalized local cohomology modules is shown and the result generalizes the corresponding result for local cohomology modules.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.455-465
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• 2020

We introduce the concepts of the left purity, right purity, quasi-purity, bipurity, left weak purity and right weak purity of ordered ideals of ordered semirings and use them to characterize regular ordered semirings, left weakly regular ordered semirings, right weakly regular ordered semirings and fully idempotent ordered semirings.

• Journal of Korean Society for Quality Management
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• v.24 no.4
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• pp.70-89
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• 1996

This paper discusses an optimal burn -in procedure to minimize total costs based on the assumption that some of the components are weak for stress and deteriorate faster than the main components. The procedure will define the costs of burn-in errors. An ideal burn-in consists of process in which all weak (substandard) components and no main (standard) components fail. In practice, the burn-in errors could occur for some reasons. For example, it is impossible to eliminate all weak components through burn-in, due to a nonzero proportion of defectives of the components. Probability model and cost function model are formulated to find the optimal burn-in time that minimizes the expected total cost. Several examples are included to show how to use the results.

• Journal of Korean Elementary Science Education
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• v.23 no.2
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• pp.131-140
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• 2004

Many idealizations and ideal conditions in physics have been an important role in understanding of the basic physics concepts and in solving physics problems. The purpose of this study was to explore the relationships of pre-service teachers' misconception of heat with their understanding of the ideal conditions involved in solving problems of heat and temperature. Test instruments were composed of two parts. One part was asked to answer the heat conceptions, the other to write statements in relations to ideal condition hidden in the process of heat problems solving. For this study, pre-service teachers who are in four major courses in the University of Education in a local city were selected and total numbers of pre-service teachers were 108 students. The framework was developed for classifying pre-service teachers response of open items of ideal conditions of heat domains. According to the framework, each types of response were coded, analyzed and processed with a SPSS/PC program. The results are as the followings. In the heat conceptions, most of students showed correct response, and there was no significant differences between major courses. In understanding of ideal conditions, students' responses of "idealized condition relevant to problem" showed 65.2％ of them, and "not relevant idealized conditions" 15.5％, and no response 12.2%. In the 15.5% of students "not relevant idealized conditions", 10.5％ of them did not explained correctly conditions, just simply 2.7％ stated the laws in physics or formula, 1.6% generally, but irrelevantly described the idealized conditions. More importantly pre-service teachers showed very weak correlation between heat conception and understanding of ideal condition. Although we concluded there were no significant relationships of heat conception in understanding of ideal conditions in thermodynamics domain, these suggest that many other factors may influence understanding of ideal conditions in physics.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.397-420
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• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.