• Kyungpook Mathematical Journal
• /
• v.47 no.2
• /
• pp.227-237
• /
• 2007

We define weak distributive $n$-semilattices and $n$-lattices, using variants of the absorption law and those of the distributive law. From a weak distributive $n$-semilattice, we construct direct system of subalgebras which are weak distributive $n$-lattices and show that its direct limit is a reflection of the category $wDn$-SLatt of the weak distributive $n$-semilattices.

• Journal of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.217-225
• /
• 1996

An orthomodular lattice (abbreviated by OML) is an ortholattice L which satisfies the orthomodular law: if x $\leq$ y, then $y = x \vee (x' \wedge y)$ [5]. A Boolean algebra B is an ortholattice satisfying the distributive law : $x \vee (g \wedge z) = (x \vee y) \wedge (x \vee z) \forall x, y, z \in B$.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.9 no.2
• /
• pp.115-127
• /
• 2009

In the present paper we introduce and study L-pre-$T_0$-, L-pre-$T_1$-, L-pre-$T_2$ (L-pre-Hausdorff)-, L-pre-$T_3$ (L-pre-regularity)-, L-pre-$T_4$ (L-pre-normality)-, L-pre-strong-$T_3$-, L-pre-strong-$T_4$-, L-pre-$R_0$-, L-pre-$R_1$-separation axioms in (2, L)-topologies where L is a complete residuated lattice.Sometimes we need more conditions on L such as the completely distributive law or that the "$\bigwedge$" is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results(see[1,2]) are generalized and new consequences are obtained.

• Journal of Educational Research in Mathematics
• /
• v.21 no.3
• /
• pp.239-259
• /
• 2011

This study investigated the elementary school students' ability on the algebraic reasoning as generalized arithmetic. It analyzed the written responses from 648 second graders, 688 fourth graders, and 751 sixth graders using tests probing their understanding of the properties of whole number operations. The result of this study showed that many students did not recognize the properties of operations in the problem situations, and had difficulties in applying such properties to solve the problems. Even lower graders were quite successful in using the commutative law both in addition and subtraction. However they had difficulties in using the associative and the distributive law. These difficulties remained even for upper graders. As for the associative and the distributive law, students had more difficulties in solving the problems dealing with specific numbers than those of arbitrary numbers. Given these results, this paper includes issues and implications on how to foster early algebraic reasoning ability in the elementary school.

• Communications of Mathematical Education
• /
• v.25 no.2
• /
• pp.473-495
• /
• 2011

Across the secondary school, students deal with the algebraic conditions like as identity, inverse, commutative law, associative law and distributive law. The algebraic structures, group, ring and field, are determined by these algebraic conditions. But the conditioning of these algebraic structures are not mentioned at all, as well as the meaning of the algebraic structures. Thus, students is likely to be considered the algebraic conditions as productions from the number sets. In this study, we systematize didactically the meanings of algebraic conditions and algebraic structures, considering connections between the number systems and the solutions of the equation. Didactically systematizing is to construct the model for student's natural mental activity, that is, to construct the stream of experience through which students are considered mathematical concepts as productions from necessities and high probability. For this purpose, we develop the program for the gifted, which its objective is to teach the meanings of the number system and to grasp the algebraic structure conceptually that is guaranteed to solve equations. And we verify the effectiveness of this developed program using didactical experiment. Moreover, the program can be used in ordinary students by replacement the term 'algebraic structure' with the term such as identity, inverse, commutative law, associative law and distributive law, to teach their meaning.

• Journal of Convergence for Information Technology
• /
• v.7 no.3
• /
• pp.65-71
• /
• 2017

The quantum logic was introduced by G. Birkhoff and 1. von Neumann in order to study projections of a Hilbert space for a formulation of quantum mechanics, and Husimi proposed orthomodular law and orthomodular lattices to complement the quantum logic. Abott introduced orthoimplication algebras and its properties to investigate an implication of orthomodular lattice. The commuting relation is an important property on orthomodular lattice which is related with the distributive law and the modular law, etc. In this paper, we define a binary operation on orthoimplication algebra and the greatest lower bound by using this operation and research some properties of this operation. Also we define a homomorphism and characterize the commuting relation of orthoimplication algebra by the homomorphism.

• The Korean Journal of Franchise Management
• /
• v.9 no.3
• /
• pp.31-43
• /
• 2018

Purpose - This study examines the role of foodservice franchisee's perceived justice(distributive, procedural, and interactional) in developing long-term orientation to franchisor and investigate the mediating role of cohesiveness and relationship satisfaction in the relationship between franchisee's perceived justice and long-term orientation to franchisor. Research design, data, and methodology - We collected data from managers and owners in foodservice franchisees located in Seoul, Korea. Among a total of 500 questionnaires, 500 questionnaires were returned. After excluding 36 invalid respondent questionnaires, 496 valid questionnaires(response rate of 99.2%) were analyzed using frequency, confirmatory factor analysis, correlations analysis, and structural equation modeling with SPSS 21 and SmartPLS 3.0. Result - The findings of this study are as follows: First, distributive justice and interactional justice had positive effects on cohesiveness, but procedural justice did not. Second, distributive justice and interactional justice had positive effects on relationship satisfaction, but procedural justice did not. Third, cohesiveness and relationship satisfaction had positive effects on franchisee's long-term orientation to franchisor. Conclusions - The implications of this study are as follows. First, this study found that procedural justice can create a high cohesiveness and identification of franchisee and also maintain a cooperative relationship with the franchisor. Second, this findings suggest that the perceived distributional and interactional justice can improve the satisfaction with the franchisor and thus positively influence the intention to maintain the relationship and the intention to recontract. Third, the results of this study indicate that the cohesiveness of franchisees can play a pivotal role to improve their satisfaction with the franchisor and pursue mutual development by continuously maintaining stable business relationship with franchisor. The findings of this study are subject to at least three limitations. First, the research subject is limited to the food service franchise shops in Seoul area, so the sample was not nationally representative of the franchise stores. Second, the perceived fairness is measured only from the point of view of the franchisee, and this study has a limitation to examine the difference between the perceived franchisee's and franchisor's justice. Third, Future research needs to identify more closely the relationships between perceived fairness and long-term orientation by gathering specific quantitative data such as the renewal rate and the business performance.

• THE INTERNATIONAL COMMERCE & LAW REVIEW
• /
• v.13
• /
• pp.1013-1032
• /
• 2000

At present, the scale of Electronic Commerce through internet has been rapidly increasing due to the development of information & communication technology, and aggregated to 2.4 billion dollar in America last year (1998). The market scale of worldwide electronic commerce is also presumed to be about 130 billion dollar in 2000, and to occupy more than 20% of the whole world trade in world 2020. Since the right of trademark, despite of being effective only in registered nations on the principle of territorialism, is unified on the cyber space of internet without domestic barrier or local limitation which make it easier to conduct the distribution of information rapidly through the address-internet domain name, those are very important that the systematic dispute-solving plan on problems such as decision of its Act and international jurisdiction to be established, in an effort to prevent the newly emerging dispute instances such as trademark infringement and improper competitiveness. In addition, it is natural that on the threshold of the electronic commerce age which formed with an unified area without the worldwide specific regulation, each country including us makes haste with the enactment of "electronic commerce Act" aiming at coming into force in 1999, in keeping with getting through "non-tariff law on electronic commerce" by U. S. parliament on May, 1998. In view of the properties of electronic commerce transactions through internet, there are the large curtailment of distributive channel, surmounting of restrictions on transaction area, space and time and the easy feedback with consumer and the cheap-required capital, from which the problems may arise - registration of trademark, the trademark infringement of domain name and the protection of prestigious trademark. Therefore, it is necessary to take the counter-measure, with a view of reviewing the infringement of trademark and domain name and the instances of each national precedent and to preventing the disputes. The improvement of the persistent system should be needed to propel the harmonious protection of those holding trademark right's credit and demanders' expectant profit by way of the righteous use of trademark.

• Journal of Elementary Mathematics Education in Korea
• /
• v.21 no.1
• /
• pp.1-22
• /
• 2017

The properties of arithmetic are considered as essential to understand the principles of calculation and develop effective strategies for calculation in the elementary school level, thanks to agreement on early algebra. Therefore elementary students' misunderstanding of the properties of arithmetic might cause learning difficulties as well as misconcepts in their following learning processes. This study aims to provide elementary teachers a part of pedagogical content knowledge about the properties of arithmetic and to induce some didactical implications for teaching the properties of arithmetic in the elementary school level. To do this, elementary school mathematics textbooks since the period of the first curriculum were analyzed. These results from analysis show which properties of arithmetic have been taught, when they were taught, and how they were taught. Based on them, some didactical implications were suggested for desirable teaching of the properties of arithmetic.

• Journal of Convergence for Information Technology
• /
• v.9 no.7
• /
• pp.14-24
• /
• 2019

It is necessary to look into multiple subjects, such as effectiveness, laws and polices of blockchain in order to easily accept blockchain technology in small and mid-sized enterprises(SME). This study analyzes the positive effects of applying the block chain to SMEs, examines the laws and policies required to apply them, and identifies the tasks. As a result, we confirmed that it can create positive effects such as optimizing supply chain management, simplifying import and export process documents, improving product quality, facilitating flow of funds, and improving transaction reliability. Also, we confirmed that it is necessary to improve the basic law of electronic transaction, electronic commerce law, electronic financial transaction law, personal information protection legislation, and needs policy supplement for platform development, education system for SMEs, transaction standardization guidelines, tax reduction policy, and block chain research and development. More extensive practical research and specific individual legal studies are needed in the future.