• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.53-67
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• 2019

The notions of closed elements and dense elements are introduced in BE-algebras. Characterization theorems of closed elements and closed filters are obtained. The notion of dense elements is introduced in BE-algebras. Dense BE-algebras are characterized with the help of maximal filters and congruences. The concept of D-filters is introduced in BE-algebras. A set of equivalent conditions is derived for every D-filter to become a closed filter.

• Journal of the Korean Institute of Telematics and Electronics
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• v.13 no.6
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• pp.20-23
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• 1976

A boolean algebra method for computing the reliability in a communication network is prosented. Given the set of all simple paths between two nodes in a network, the terminal reliability can be symbolically computed by the Boolean operation which is named parallel operation. The method seems to be promising for both oriented and nonoriented network.

• Communications of Mathematical Education
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• v.27 no.1
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• pp.1-17
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• 2013

This work started with recent students' conception on Linear Algebra. We were trying to help their understanding of Linear Algebra concepts by adding visualization tools. To accomplish this, we have developed most of needed tools for teaching of Linear Algebra class. Visualizing concepts of Linear Algebra is not only an aid for understanding but also arouses students' interest on the subject for a better comprehension, which further helps the students to play with them for self-discovery. Therefore, visualizing data should be prepared thoroughly rather than just merely understanding on static pictures as a special circumstance when we would study visual object. By doing this, we carefully selected GeoGebra which is suitable for dynamic visualizing and Sage for algebraic computations. We discovered that this combination is proper for visualizing to be embodied and gave a variety of visualizing data for undergraduate mathematics classes. We utilized GeoGebra and Sage for dynamic visualizing and tools used for algebraic calculation as creating a new kind of visual object for university math classes. We visualized important concepts of Linear Algebra as much as we can according to the order of the textbook. We offered static visual data for understanding and studied visual object and further prepared a circumstance that could create new knowledge. We found that our experience on visualizations in Linear Algebra using Sage and GeoGebra to our class can be effectively adopted to other university math classes. It is expected that this contribution has a positive effect for school math education as well as the other lectures in university.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.513-528
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• 2017

The concept of weak implicative filters is introduced in BE-algebras. Some characterizations of weak implicative filters are derived in terms of filters of a BE-algebra. Fuzzification is applied to the class of weak implicative filters. Some properties of fuzzy weak implicative filters are studied with respect to fuzzy relations and homomorphisms. The notion of triangular normed fuzzy weak implicative filters is introduced in BE-algebras and their properties are studied.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.483-494
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• 2012

In this paper we study properties of commutative BE-algebras and we give the construction of quotient (X/I; *, I) of a commutative BE-algebra X via an obstinate ideal I of X. We construct upper semilattice and prove that is a nearlattice. Finally we define and study commutative ideals in BE-algebras.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.193-199
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• 1993

A hereditary $C^{*}$-subalgebra B of a $C^{*}$-algebra A is said to be full if B is not contained in any proper closed two-sided ideal in A, so each hereditary $C^{*}$-subalgebra of a simple $C^{*}$-algebra is always full. It is well known that every $C^{*}$-algebra is strong Morita equivalent to its full hereditary $C^{*}$-subalgebra, but the strong Morita equivalence of a $C^{*}$-algebra A and its hereditary $C^{*}$-subalgebra B does not imply the fullness of B, ingeneral. We present the following lemma for our computational convenience in the course of the proof of the main theorem. Note that $L_{B}$, $L_{B}$$^{*}$ and $L_{B}$ $L_{B}$$^{*}$ are all .alpha.-invariant whenever B is .alpha.-invariant under the action .alpha. of G.a. of G.a. of G.a. of G.f G.

• Honam Mathematical Journal
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• v.37 no.2
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• pp.207-219
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• 2015

As a generalization of BH-algebras, the notion of pseudo BH-algebra is introduced, and some of their properties are investigated. The notions of pseudo ideals, pseudo atoms, pseudo strong ideals, and pseudo homomorphisms in pseudo BH-algebras are introduced. Characterizations of their properties are provided. We show that every pseudo homomorphic image and preimage of a pseudo ideal is also a pseudo ideal. Any pseudo ideal of a pseudo BH-algebra can be decomposed into the union of some sets. The notion of pseudo complicated BH-algebra is introduced and some related properties are obtained.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.1-11
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• 2000

The non-commutative torus $A_{\omega}=C^*(\mathbb{Z}^n,{\omega})$ may be realized as the $C^*$-algebra of sections of a locally trivial $C^*$-algebra bundle over $\widehat{S_{\omega}}$ with fibres $C^*(\mathbb{Z}^n/S_{\omega},{\omega}_1)$ for some totally skew multiplier ${\omega}_1$ on $\mathbb{Z}^n/S_{\omega}$. It is shown that $A_{\omega}{\otimes}M_l(\mathbb{C})$ has the trivial bundle structure if and only if $\mathbb{Z}^n/S_{\omega}$ is torsion-free.

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.179-183
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• 1988

In this paper we study a $C^{*}$-dynamical system (A, G, .alpha.) where A is a UHF-algebra, G is a finite abelian group and .alpha. is a *-automorphic action of product type of G on A. In [2], A. Kishimoto considered the case G= $Z_{n}$, the cyclic group of order n and investigated a condition in order that the fixed point algebra $A^{\alpha}$ of A under the action .alpha. is UHF. In later N.J. Munch studied extremal tracial states on $A^{\alpha}$ by employing the method of A. Kishimoto [3], where G is a finite abelian group. Generally speaking, when G is compact (not necessarily discrete and abelian), $A^{\alpha}$ is an AF-algebra and its ideal structure was well analysed by N. Riedel [4]. Here we obtain some conditions for $A^{\alpha}$ to be UHF, where G is a finite abelian group, which is an extension of the result of A. Kishimoto.oto.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.615-624
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• 1998

We consider a generalization of [1. theorem 2.5]. We give a description of the element of $_{\mathcal I}^l$(resp. $_{\mathcal I} ^r$), where A and B are left (resp. right)${\mathcal I}$-ideals of an IS-algebra X. For a nonempty left (resp. right) stable, we obtain a condition for $_{\mathcal I}^l$(resp. $_{\mathcal I}^l$) to be closed. We give a characterization of a closed $\mathcal I$-ideal in an IS-algebra, and show that in a finite IS-algebra, every $\mathcal I$-ideal is closed.