• Journal of the Korean Institute of Telematics and Electronics S
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• v.36S no.6
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• pp.9-16
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• 1999

In this paper, an efficient algorithm for generation do Lempel's D-homomorphism. This number of exclusive-or operations required to generate the next bit for de Bruijn sequences of order n from a de Bruijm function of order k is shown to be approximately $k(2^{W(n-k)}-1)$where W(r) is the number of one's in the binary representation of r: therefore, the number of required operations can reduced to k if the de Bruijn function is selected appropriately.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1305-1319
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• 2014

A submodule N of a right R-module M is called coneat if for every simple right R-module S, any homomorphism $N{\rightarrow}S$ can be extended to a homomorphism $M{\rightarrow}S$. M is called coneat-flat if the kernel of any epimorphism $Y{\rightarrow}M{\rightarrow}0$ is coneat in Y. It is proven that (1) coneat submodules of any right R-module are coclosed if and only if R is right K-ring; (2) every right R-module is coneat-flat if and only if R is right V -ring; (3) coneat submodules of right injective modules are exactly the modules which have no maximal submodules if and only if R is right small ring. If R is commutative, then a module M is coneat-flat if and only if $M^+$ is m-injective. Every maximal left ideal of R is finitely generated if and only if every absolutely pure left R-module is m-injective. A commutative ring R is perfect if and only if every coneat-flat module is projective. We also study the rings over which coneat-flat and flat modules coincide.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1095-1106
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• 2020

The purpose of this paper is to introduce a new class of rings that is closely related to the class of pseudo-Krull domains. Let 𝓗 = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. Let R ∈ 𝓗 be a ring with total quotient ring T(R) and define 𝜙 : T(R) → R_Nil(R) by ${\phi}({\frac{a}{b}})={\frac{a}{b}}$ for any a ∈ R and any regular element b of R. Then 𝜙 is a ring homomorphism from T(R) into R_Nil(R) and 𝜙 restricted to R is also a ring homomorphism from R into R_Nil(R) given by ${\phi}(x)={\frac{x}{1}}$ for every x ∈ R. We say that R is a 𝜙-pseudo-Krull ring if 𝜙(R) = ∩ R_i, where each R_i is a nonnil-Noetherian 𝜙-pseudo valuation overring of 𝜙(R) and for every non-nilpotent element x ∈ R, 𝜙(x) is a unit in all but finitely many R_i. We show that the theories of 𝜙-pseudo Krull rings resemble those of pseudo-Krull domains.

• East Asian mathematical journal
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• v.23 no.1
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• pp.23-36
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• 2007

In this paper we consider the fuzzy ideals of N-group G where N is a nearring. We introduce fuzzy ideal ${\theta}_{\mu}$ of the quotient N-group $G/{\mu}$ with respect to a fuzzy ideal $\mu$ of G. If $\mu$ is a fuzzy ideal of G and $\theta$ a fuzzy ideal of $G/{\mu}$ such that ${\theta}_{\mu}\;{\subseteq}\;{\theta}$ and ${\theta}_{\mu}(0)\;=\;{\theta}(0)$, then corresponding ${\sigma}_{\theta}\;:\;G\;{\rightarrow}\;[0,\;1]$ is defined and proved that it is a fuzzy ideal of G such that ${\mu}\;{\subseteq}\;{\sigma}_{\theta}$ and ${\mu}(0)\;=\;{\sigma}_{\theta}(0)$. We also prove some results on homomorphisms and fuzzy ideals of N-groups. The image and preimage of fuzzy ideal $\mu$ under N-group homomorphism were studied. Finally it is obtained that if $f\;:\;G\;{\rightarrow}\;G^1$ is an epimorphism of N-groups, then there is an order preserving bijection between the fuzzy ideals of $G^1$ and the fuzzy ideals of G that are constant on kerf. Some examples related to these concepts were illustrated.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.8
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• pp.1472-1491
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• 2011

As used product transactions are currently on the rise, the demand for transactions of secondhand digital content will grow in the future; thus, learning to make secure transactions while avoiding cyber attacks becomes an important issue. In this paper, we combine the new buyer's secret key, the new buyer's watermark to embed in resold digital content, and the reseller's encrypted watermark, which can prove legal ownership of the reseller. Using the privacy homomorphism property of RSA and exponential calculus, the original seller of digital content can verify the legality of the reseller and the new buyer. We also reduced the load of encryption/decryption digital content using a partial encryption/decryption algorithm to make our protocol more efficient and practical. In the proposed protocol, the seller is not able to conduct piracy and easily frame any other innocent secondhand buyer when a case of piracy is found. In fact, piracy can be clearly traced using the privacy homomorphism property of RSA and the embedded watermark mechanism. Further, in the proposed protocol, the seller himself can trace the piracy using exponential calculus. Since it is unnecessary to trust third party participation, the conspiracy problem is resolved and the new buyer is not required to participate in the dispute. Moreover, the seller, reseller and new buyer can simultaneously benefit from the secondhand transaction.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.933-944
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• 2013

Based on the four kinds of theoretical definitions of the continuous module homomorphism between random locally convex modules, we first show that among them there are only two essentially. Further, we prove that such two are identical if the family of $L^0$-seminorms for the former random locally convex module has the countable concatenation property, meantime we also provide a counterexample which shows that it is necessary to require the countable concatenation property.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.149-161
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• 2011

Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the following Jensen type functional equation: $$f({\frac{x+y}{2}})+f({\frac{x-y}{2}})=f(x)$$.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.349-356
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• 2006

The aim of this paper is to endow a monoid structure on the set S of all oriented knots(links) under the operation ${\biguplus}$, called addition of knots. Moreover, we prove that there exists a homomorphism of monoids between ($S_d,\;{\biguplus}$) to (N, +), where $S_d$ is a subset of S with an extra condition and N is the monoid of non negative integers under usual addition.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.233-245
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• 2019

Cyclic hypergroups are of great importance due to their applications to many field in mathematics. In this paper, we classify all polygroups of order less than six where each of its non-identity elements is a generator.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.73-88
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• 2004

A punctured torus $\Sigma(1,1)$ is a building block of oriented surfaces. The goal of this paper is to formulate the matrix presentations of elements of the Teichmuller space of a punctured torus. Let $\cal{C}$ be a matrix presentation of the boundary component of $\Sigma(1,1)$.In the level of the matrix group $\mathbb{SL}$($\mathbb2,R$) we shall show that the trace of $\cal{C}$ is always negative.