• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.451-459
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• 2023

We give a characterization of zero divisors of the ring C[a, b]. Using the Weierstrass approximation theorem, we completely characterize topological divisors of zero of the Banach algebra C[a, b]. We also characterize the zero divisors and topological divisors of zero in ℓ^∞. Further, we show that zero is the only zero divisor in the disk algebra 𝒜 (𝔻) and that the class of singular elements in 𝒜 (𝔻) properly contains the class of topological divisors of zero. Lastly, we construct a class of topological divisors of zero of 𝒜 (𝔻) which are not zero divisors.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1057-1073
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• 2008

We present an explicit Eta pairing approach for computing the Tate pairing on general divisors of hyperelliptic curves $H_d$ of genus 2, where $H_d\;:\;y^2+y=x^5+x^3+d$ is defined over ${\mathbb{F}}_{2^n}$ with d=0 or 1. We use the resultant for computing the Eta pairing on general divisors. Our method is very general in the sense that it can be used for general divisors, not only for degenerate divisors. In the pairing-based cryptography, the efficient pairing implementation on general divisors is significantly important because the decryption process definitely requires computing a pairing of general divisors.

• Kyungpook Mathematical Journal
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• v.51 no.1
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• pp.37-42
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• 2011

Let M be an R-module and S a semigroup. Our goal is to discuss zero-divisors of the semigroup module M[S]. Particularly we show that if M is an R-module and S a commutative, cancellative and torsion-free monoid, then the R[S]-module M[S] has few zero-divisors of size n if and only if the R-module M has few zero-divisors of size n and Property (A).

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.717-734
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• 1998

In the present paper is presented a new matrix pencil-based numerical approach achieving the computation of the elemen-tary divisors of a given matrix $A \in C^{n\timesn}$ This computation is at-tained without performing similarity transformations and the whole procedure is based on the construction of the Piecewise Arithmetic Progression Sequence(PAPS) of the associated pencil $\lambda I_n$ -A of matrix A for all the appropriate values of $\lambda$ belonging to the set of eigenvalues of A. This technique produces a stable and accurate numerical algorithm working satisfactorily for matrices with a well defined eigenstructure. The whole technique can be applied for the computation of the first second and Jordan canonical form of a given matrix $A \in C^{n\timesn}$. The results are accurate for matrices possessing a well defined canonical form. In case of defective matrices indications of the most appropriately computed canonical form. In case of defective matrices indication of the most appropriately computed canonical form are given.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.221-233
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• 2009

In this article, we generalize a well-known result of Hebisch and Weinert that states that a finite semidomain is either zerosumfree or a ring. Specifically, we show that the class of commutative semirings S such that S has nonzero characteristic and every zero-divisor of S is nilpotent can be partitioned into zerosumfree semirings and rings. In addition, we demonstrate that if S is a finite commutative semiring such that the set of zero-divisors of S forms a subtractive ideal of S, then either every zero-sum of S is nilpotent or S must be a ring. An example is given to establish the existence of semirings in this latter category with both nontrivial zero-sums and zero-divisors that are not nilpotent.

• East Asian mathematical journal
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• v.39 no.3
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• pp.349-354
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• 2023

The motivation in this paper comes from the recent results about Bell inequalities and topological insulators from group theory. Symmetries which are interested in group theory could be mainly used to find material structures. In this point of views, we study group extending by adding one relator which is easily called an equation. So a relative group extension by a adding relator is aspherical if the natural injection is one-to-one and the group ring has no zero divisor. One of concepts of asphericity means that a new group by a adding relator is well extended. Also, we consider that several equations and relative presentations over torsion-free groups are related to zero divisors.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1279-1285
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• 2005

Here we generalize previous work by Eisenbud-Harris and Farkas in order to prove that certain Brill-Noether divisors on the moduli space of curves have distinct supports. From this fact we deduce non-trivial regularity results for a higher co dimensional Brill-Noether locus and for the general $\frac{g+1}{2}$-gonal curve of odd genusg.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1677-1697
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• 2017

The purpose of this paper is to investigate the close relation between Okounkov bodies and Zariski decompositions of pseudoeffective divisors on smooth projective surfaces. Firstly, we completely determine the limiting Okounkov bodies on such surfaces, and give applications to Nakayama constants and Seshadri constants. Secondly, we study how the shapes of Okounkov bodies change as we vary the divisors in the big cone.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.567-580
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• 1999

We prove two variants of a base-point-free pencil trick, which are similar in the spirit of the proof, and apply them to the study of special divisors on a smooth plane curve involving a theorem of Max Noether.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.541-550
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• 2002

In this Paper, We look at 3 Simple function L assigning to an integer n the smallest positive integer n such that any product of n consecutive numbers is divisible by n. Investigated are the interesting properties of the function. The function L(n) is completely determined by L(p$\^$k/), where p$\^$k/ is a factor of n, and satisfies L(m$.$n) $\leq$ L(m)+L(n), where the equality holds for infinitely many cases.