• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.769-784
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• 2022

The main theme of this present paper is to study ordered semigroups in the context of anti-hybrid interior ideals. The notion of anti-hybrid interior ideals in ordered semigroups is introduced. We prove that the concepts of ideals and interior coincide in some particular classes of ordered semigroups; regular, intra-regular, and semisimple. Finally, the characterization of semisimple ordered semigroups in terms of anti-hybrid interior ideals is considered.

• Honam Mathematical Journal
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• v.28 no.2
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• pp.185-196
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• 2006

A scheme based on the cryptography for enforcing multilevel security in a system where hierarchy is represented by a partially ordered set was first introduced by Akl et al. But the key generation algorithm of Akl et al. is infeasible when there is a large number of users. In 1985, MacKinnon et al. proposed a paper containing a condition which prevents cooperative attacks and optimizes the assignment in order to overcome this shortage. In 2005, Kim et al. proposed key management systems for multilevel security using one-way hash function, RSA algorithm, Poset dimension and Clifford semigroup in the context of modern cryptography. In particular, the key management system using Clifford semigroup of imaginary quadratic non-maximal orders is based on the fact that the computation of a key ideal $K_0$ from an ideal $EK_0$ seems to be difficult unless E is equivalent to O. We, in this paper, show that computing preimages under the bonding homomorphism is not difficult, and that the multilevel cryptosystem based on the Clifford semigroup is insecure and improper to the key management system.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.4
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• pp.605-610
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• 2013

A cryptography for enforcing hierarchic groups in a system where hierarchy is represented by a partially ordered set was introduced by Akl et al. But the key generation algorithm of Akl et al. is infeasible when there is a large number of users. To overcome this shortage, in 1985, MacKinnon et al. proposed a paper containing a condition which prevents cooperative attacks and optimizes the assignment. In 2005, Kim et al. proposed the key management systems for using one-way hash function, RSA algorithm, poset dimension and Clifford semigroup in the context of modern cryptography, the key management system using Clifford semigroup of imaginary quadratic non-maximal orders. We, in this paper, show that Kim et al. cryptosystem is insecure in some reasons and propose a revised cryptosystem.

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.869-889
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• 2015

Let ${\Gamma}^+$ be the positive cone in a totally ordered abelian group ${\Gamma}$, and ${\alpha}$ an action of ${\Gamma}^+$ by extendible endomorphisms of a $C^*$-algebra A. Suppose I is an extendible ${\alpha}$-invariant ideal of A. We prove that the partial-isometric crossed product $\mathcal{I}:=I{\times}^{piso}_{\alpha}{\Gamma}^+$ embeds naturally as an ideal of $A{\times}^{piso}_{\alpha}{\Gamma}^+$, such that the quotient is the partial-isometric crossed product of the quotient algebra. We claim that this ideal $\mathcal{I}$ together with the kernel of a natural homomorphism $\phi:A{\times}^{piso}_{\alpha}{\Gamma}^+{\rightarrow}A{\times}^{iso}_{\alpha}{\Gamma}^+$ gives a composition series of ideals of $A{\times}^{piso}_{\alpha}{\Gamma}^+$ studied by Lindiarni and Raeburn.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1275-1283
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• 2010

If the Wiener-Hopf $C^*$-algebra W(G,M) for a discrete group G with a semigroup M has the uniqueness property, then the structure of it is to some extent independent of the choice of isometries on a Hilbert space. In this paper we show that if the Wiener-Hopf $C^*$-algebra W(G,M) of a partially ordered group G with the positive cone M has the uniqueness property, then (G,M) is weakly unperforated. We also prove that the Wiener-Hopf $C^*$-algebra W($\mathbb{Z}$, M) of subsemigroup generating the integer group $\mathbb{Z}$ is isomorphic to the Toeplitz algebra, but W($\mathbb{Z}$, M) does not have the uniqueness property except the case M = $\mathbb{N}$.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.349-361
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• 2015

A fence is an ordered set that the order forms a path with alternating orientation. Let F = (F;${\leq}$) be a fence and let OT(F) be the semigroup of all order-preserving self-mappings of F. We prove that OT(F) is coregular if and only if ${\mid}F{\mid}{\leq}2$. We characterize all coregular elements in OT(F) when F is finite. For any subfence S of F, we show that the set COTS(F) of all order-preserving self-mappings in OT(F) having S as their range forms a coregular subsemigroup of OT(F). Under some conditions, we show that a union of COTS(F)'s forms a coregular subsemigroup of OT(F).

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.315-321
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• 1996

Recently, N. Kehayopulu [4] introduced the concepts of weakly prime ideals of ordered semigroups. In this paper, we define the concepts of left(right) weakly prime and left(right) semiregular. Also we investigate the properties of them.