• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.497-505
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• 2013

The noncommutative Singer-Wermer conjecture states that every derivation on a Banach algebra (possibly noncommutative) leaves primitive ideals of the algebra invariant. This conjecture is still an open question for more than thirty years. In this note, we approach this question via some sufficient conditions for the separating ideal of ${\phi}$-derivations to be nilpotent. Moreover, we show that the spectral boundedness of ${\phi}$-derivations implies that they leave each primitive ideal of Banach algebras invariant.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.123-135
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• 2023

It is proved that there is a one to one correspondence between representations of C^*-ternary ring M and C^*-algebra 𝒜(M). We discuss primitive and modular ideals of a C^*-ternary ring and prove that a closed ideal I is primitive or modular if and only if so is the ideal 𝒜(I) of 𝒜(M). We also show that a closed ideal in M is primitive if and only if it is the kernel of some irreducible representation of M. Lastly, we obtain approximate identity characterization of strongly quasi-central C^*-ternary ring and the ideal structure of the TRO V ⊗^tmin B for a C^*-algebra B.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.1-23
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• 2019

Let ${\mathcal{G}}$ be an ultragraph and let $C^*({\mathcal{G}})$ be the associated $C^*$-algebra introduced by Tomforde. For any gauge invariant ideal $I_{(H,B)}$ of $C^*({\mathcal{G}})$, we approach the quotient $C^*$-algebra $C^*({\mathcal{G}})/I_{(H,B)}$ by the $C^*$-algebra of finite graphs and prove versions of gauge invariant and Cuntz-Krieger uniqueness theorems for it. We then describe primitive gauge invariant ideals and determine purely infinite ultragraph $C^*$-algebras (in the sense of Kirchberg-Rørdam) via Fell bundles.

• East Asian mathematical journal
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• v.16 no.1
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• pp.71-79
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• 2000

We show that the intersection of two standard torus knots of type (${\lambda}_1$, ${\lambda}_2$) and (${\beta}_1$, ${\beta}_2$) induces an automorphism of the cyclic group ${\mathbb{Z}}_d$, where d is the intersection number of the two torus knots and give an elementary proof of the fact that all non-trivial torus knots are strongly invertiable knots. We also show that the intersection of two standard knots on the 3-torus $S^1{\times}S^1{\times}S^1$ induces an isomorphism of cyclic groups.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.47-52
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• 2018

Let ${\delta}$ be a derivation in a noetherian integral domain A. It is shown that a natural map induces a homeomorphism between the spectrum of $A[z;{\delta}]$ and the Poisson spectrum of $A[z;{\delta}]_p$ such that its restriction to the primitive spectrum of $A[z;{\delta}]$ is also a homeomorphism onto the Poisson primitive spectrum of $A[z;{\delta}]_p$.

• 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.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.53 no.4
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• pp.637-649
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• 2020

An ideal 3D primitive equation model is implemented to investigate upper ocean response to typhoons, focusing on rightward bias (RWB) which means an appearance of an intensified sea surface cooling to the right side of the typhoon track. The model has 26-stratified levels and a flat bottom (1000 m), covering a rectangular domain of about 3,060 km×3,300 km with four open boundaries. The sea water is forced by an atmospheric pressure and a gradient wind of the typhoon. The model well reproduces the RWB in previous observations and theoretical analyses. For the fast moving typhoon (FMT) (-8m/sec), the model shows that in the mixed layer (ML), the RWB in the SST noticeably appears clearly illustrating the coupling between inertial motion and wind stress, but in the subsurface layer (-100m), the RWB does not emerge since a cyclonic current field (CCF) caused by wind stress curl is primarily dominant. For the slowly moving typhoon (SMT) (-3m/sec), however, the RWB does not emerge because the coupling is weakened and the CCF is rather predominant even in the ML. In the model, we conclude that the RWB noticeably emerges in the FMT but does not emerge in the SMT related to predominance of CCF.

• Honam Mathematical Journal
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• v.26 no.3
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• pp.247-256
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• 2004

Buchmann and Williams[1] proposed a key exchange system making use of the properties of the maximal order of an imaginary quadratic field. $H{\ddot{u}}hnlein$ et al. [6,7] also introduced a cryptosystem with trapdoor decryption in the class group of the non-maximal imaginary quadratic order with prime conductor q. Their common techniques are based on the properties of the invertible ideals of the maximal or non-maximal orders respectively. Kim and Moon [8], however, proposed a key-exchange system and a public-key encryption scheme, based on the class semigroups of imaginary quadratic non-maximal orders. In Kim and Moon[8]'s cryptosystem, a non-invertible ideal is chosen as a generator of key-exchange ststem and their secret key is some characteristic value of the ideal on the basis of Zanardo et al.[9]'s quantity for ideal equivalence. In this paper we propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structure of the class semigroup of non-maximal order as finitely disjoint union of groups with some quantities correctly. And then we correct the misconceptions of Zanardo et al.[9] and analyze Kim and Moon[8]'s cryptosystem.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.33-39
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• 1994

The purpose of this paper prove the following property; Suppose A has many units (local global ring) and |A/m| > 5 for every maximal ideal $m{\subseteq}A$. Let(E, q) ${\in}$ Q(A) and $E=E_1{\bot}{\cdots}{\bot}E_t$ be an orthogonl decomposition of E with $t{\geq}2$ and $rk(E_i){\geq}1$, for $i=1,{\cdots},t$. Let $x{\in}E$ be a primitive vector. Then there exists ${\sigma}{\in}O(q)$ such that ${\sigma}(x)$ is transversal to this decomposition.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1025-1034
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• 2023

Let U be the restricted quantized enveloping algebra Ũ_q(𝖘𝖑₂) over an algebraically closed field of characteristic zero, where q is a primitive 𝑙-th root of unity (with 𝑙 being odd and greater than 1). In this paper we show that any indecomposable submodule of U under the adjoint action is generated by finitely many special elements. Using this result we describe all ideals of U. Moreover, we classify annihilator ideals of simple modules of U by generators.