• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.215-221
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• 2003

There seems to be a love-hate relationship between Brouwer's fixed point theorem and the fundamental theorem of algebra; in this note we offer one more tweak at it, and give a version of Rouches theorem.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.699-705
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• 2015

Two well known facts from elementary number theory are proven by using Bergman spaces.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.849-856
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• 2014

In this paper we introduce the notion of medial B-algebras, and we obtain a fundamental theorem of B-homomorphism for B-algebras.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.21-32
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• 2008

We introduce some notions and results which have been discussed, and we define the notion of fuzzy normal B-algebra and obtain the structure of quotient B-algebra via fuzzy normal B-algebra. Moreover, we generalize a fundamental theorem of B-homomorphism for B-algebras via fuzzy normal B-algebras.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.2
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• pp.182-186
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• 2002

We investigate the quotient structure of a product BCK-algebra and fundamental homomorphism theorem and show their some properties.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.51-62
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• 2002

The present paper gives a new construction of a quotient BCI(BCK)-algebra X/${\mu}$ by a fuzzy ideal ${\mu}$ in X and establishes the Fuzzy Homomorphism Fundamental Theorem. We show that if ${\mu}$ is a fuzzy ideal (closed fuzzy ideal) of X, then X/${\mu}$ is a commutative (resp. positive implicative, implicative) BCK(BCI)-algebra if and only if It is a fuzzy commutative (resp. positive implicative, implicative) ideal of X Moreover we prove that a fuzzy ideal of a BCI-algebra is closed if and only if it is a fuzzy subalgebra of X We show that if the period of every element in a BCI-algebra X is finite, then any fuzzy ideal of X is closed. Especiatly, in a well (resp. finite, associative, quasi-associative, simple) BCI-algebra, any fuzzy ideal must be closed.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.669-674
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• 2000

We define the terminologies for the special type of functions defined on the field $\mathbb{C}$ of complex numbers and consider the solutions of function equations containing such functions in $\mathbb{C}$.

• Journal for History of Mathematics
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• v.29 no.5
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• pp.295-314
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• 2016

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. We learned that dynamic programming in tropical algebraic geometry can be used to find the shortest path in graphs. We have also learned about the Bezout's Theorem, which is a theorem concerning the intersections of tropical plane curves, and the stable intersection principle.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.27-36
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• 2006

In this paper, we establish a generalization of fundamental homomorphism theorem in BCK-algebras by using fuzzy BCK-filters. We prove that if ${\mu}$. (resp. v) is a fuzzy BCK-filter of abounded BCK-algebra X (resp. Y), then $\frac{X{\times}Y}{{\mu}{\times}v}{\approxeq}X/{\mu}{\times}Y/v;\;and\;if\;{\mu}$ and F is a BCK-filter in a bounded BCK-algebra X such that $F/{\mu}$ is a BCK-filter of $X/{\mu}$, then $\frac{X/{\mu}}{F/{\mu}}{\approxeq}X/F$.

• Journal of the Korea Computer Graphics Society
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• v.6 no.1
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• pp.37-50
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• 2000

Using the complex formulation of plane curves which R. T. Farouki introduced, we can identify any plane polynomial curve with only a polynomial with complex coefficients. In this paper, using the well-known fundamental theorem of algebra, we completely factorize the polynomial over the complex number field C and from the completely factorized form of the polynomial, we find a new necessary and sufficient condition for a plane polynomial curve to be a Pythagorean-hodograph curve, obseving the set of all roots of the complex polynomial corresponding to the plane polynomial curve. Applying this method to space polynomial curves in the three dimensional Minkowski space $R^{2,1}$, we also find the necessary and sufficient condition for a polynomial curve in $R^{2,1}$ to be a PH curve in a new finer form and characterize all possible curves completely.