• Korean Journal of Mathematics
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• 제12권1호
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• pp.49-54
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• 2004

In this paper we introduce the notion of quotient Boolean algebra and study the relation between the ideals of Boolean algebra ${\wp}(S)$ and the ideals of quotient Boolean algebra ${\wp}(S)/I$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권2호
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• pp.71-78
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• 2000

Any Hausdoroff space on a set which has at least two points a regular closed Boolean algebra different from the indiscrete regular closed Boolean algebra as indiscrete space. The Sierpinski space and the space with finite complement topology on any infinite set etc. do the same. However, there is $T_{0}$ space which does the same with Hausdorpff space as above. The regular closed Boolean algebra in a topological space is isomorphic to that algebra in the space with its open extension topology.

• 대한수학회지
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• 제43권1호
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• pp.77-86
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• 2006

We consider the set of commuting pairs of matrices and their preservers over binary Boolean algebra, chain semiring and general Boolean algebra. We characterize those linear operators that preserve the set of commuting pairs of matrices over a general Boolean algebra and a chain semiring.

• 충청수학회지
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• 제29권4호
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• pp.613-629
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• 2016

In this paper, we introduced the notion of multiplier of Boolean algebras and discuss related properties between multipliers and special mappings, like dual closures, homomorphisms on B. We introduce the notions of xed set $Fix_f(X)$ and normal ideal and obtain interconnection between multipliers and $Fix_f(B)$. Also, we introduce the special multiplier ${\alpha}_p$a nd study some properties. Finally, we show that if B is a Boolean algebra, then the set of all multipliers of B is also a Boolean algebra.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.531-536
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• 1998

It is well known that a Boolean algebra is one of the most important algebra for engineering. A fuzzy algebra, which is referred to also as a Kleen algebra, is obtained from a Boolean algebra by replacing the complementary law in the axioms of a Bloolean algebra with the Kleen's law, where the Kleen's law is a weaker condition than the complementary law. Removal of the Kleen's law from a Kleen algebra gives a De Morgan algebra. In this paper, we generate lattice structures of the above related algebraic systems having finite elements by using a computer. From the result, we could find out a hypothesis that the structure excepting for each element name between a Kleene algebra and a De Morgan algebra is the same from the lattice standpoint.

• 대한수학회지
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• 제32권3호
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• pp.531-540
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• 1995

There is much literature on the study of matrices over a finite Boolean algebra. But many results in Boolean matrix theory are stated only for binary Boolean matrices. This is due in part to a semiring isomorphism between the matrices over the Boolean algebra of subsets of a k element set and the k tuples of binary Boolean matrices. This isomorphism allows many questions concerning matrices over an arbitrary finite Boolean algebra to be answered using the binary Boolean case. However there are interesting results about the general (i.e. nonbinary) Boolean matrices that have not been mentioned and they differ somwhat from the binary case.

• 한국항행학회논문지
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• 제15권5호
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• pp.781-788
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• 2011

Sphere-packing problem은 주어진 공간에 가능한 한 많은 구(sphere)를 채울 수 있는 배열을 찾는 문제이고 covering problem은 이에 쌍대적인 최적화의 문제로 코딩이론에 적용된다. 본 논문에서는 이진 코드이론에서의 가중치(weight)와 해밍거리(Hamming distance)에 대한 개념을 부울 대수(Boolean algebra)의 개념으로 일반화한다. 부울 대수에서의 가중치와 이를 이용하여 거리함수를 정의하고, 이들의 기본적인 성질들을 밝힌다. 또한, 부울 대수에서의 sphere-packing bound와 Gilbert-Varshamov bound의 정리를 증명한다.

• 대한수학회논문집
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• 제28권1호
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• pp.1-9
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• 2013

We consider the sets of matrix ordered pairs which satisfy extremal properties with respect to Boolean rank inequalities of matrices over nonbinary Boolean algebra. We characterize linear operators that preserve these sets of matrix ordered pairs as the form of $T(X)=PXP^T$ with some permutation matrix P.

• 대한전자공학회논문지
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• 제13권6호
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• pp.20-23
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• 1976

본논문에서는 통신회로망의 신뢰도를 계산하는데 부울대수를 이용하는 방법을 제시하였다. 한 회로의 두 접합점사이의 모든 단순통로가 주어지면 병렬연산이라고 명명되는 부울대수산법에 의하여 두 단점사이의 신뢰도가 기호적으로 계산된다. 이 방법은 회로가 방향성이거나 비방향성이거나 다 효과적이다. 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.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1525-1532
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• 2011

The $m{\times}n$ Boolean matrix A is said to be of Boolean rank r if there exist $m{\times}r$ Boolean matrix B and $r{\times}n$ Boolean matrix C such that A = BC and r is the smallest positive integer that such a factorization exists. We consider the the sets of matrix ordered pairs which satisfy extremal properties with respect to Boolean rank inequalities of matrices over nonbinary Boolean algebra. We characterize linear operators that preserve these sets of matrix ordered pairs as the form of $T(X)=PXP^T$ with some permutation matrix P.