• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1333-1348
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• 2013

Given a faithful flow ${\alpha}$ on a $C^*$-algebra A, when A is ${\alpha}$-simple we will show that the closed subalgebra of A consisting of elements with non-negative Arveson spectra is maximal if and only if the crossed product of A by ${\alpha}$ is simple. We will also show how the general case can be reduced to the ${\alpha}$-simple case, which roughly says that any flow with the above maximality is an extension of a trivial flow by a flow of the above type in the ${\alpha}$-simple case. We also propose a condition of essential maximality for such closed subalgebras.

• Journal for History of Mathematics
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• v.27 no.6
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• pp.403-408
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• 2014

The interdisciplinary study addresses the G$\ddot{o}$del's ontology from the perspective of the mathematical maximality. We first investigate G$\ddot{o}$del's God having all the positive properties as the intersection of ultrafilters in his own ontological proof(1970). Regarding the axiom of choice and his compactness theorem(1930), the next part discusses the ontological meaning of the maximal rather than the maximum in terms of an episteme space. The results show that G$\ddot{o}$del's ontological arguments imply all the existence of the maximal reality, and all the human's epistemological boundedness as well.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.1-19
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• 2000

We investigate in this paper the maximality of prime ideals in rings whose simple singular left R-modules are p-injective.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.295-306
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• 2012

Let (R, $m_R$, k) be a local maximal commutative subalgebra of $M_n$(k) with nilpotent maximal ideal $m_R$. In this paper, we will construct a maximal commutative subalgebra $R^{ST}$ which is isomorphic to R and study some interesting properties related to $R^{ST}$. Moreover, we will introduce a method to construct an algebra in $MC_n$(k) with i($m_R$) = n and dim(R) = n.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.775-784
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• 2009

In 1932, Lehmer [4] gave the definition of a ternary semigroup. We can see that any semigroup can be reduced to a ternary semigroup. In this paper, we give some auxiliary results which are also necessary for our considerations and characterize the relationship between the (0-)minimal and maximal ordered lateral ideals and the lateral simple and lateral 0-simple ordered ternary semigroups analogous to the characterizations of minimal and maximal left ideals in ordered semigroups considered by Cao and Xu [2].

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.951-962
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• 2003

In this paper we address focal points and treat manifolds (M, g) whose Lorentzian metric tensors g have a spacelike $C^{0}$-hypersurface $\Sigma$ [10]. We apply Jacobi fields for such manifolds, and check the local length maximizing properties of $C^1$-geodesics. The condition of maximality of timelike curves(geodesics) passing $C^{0}$-hypersurface is studied.ied.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.476-481
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• 1991

This paper investigates the relationship between the two problems, supervisor reduction and observation function (projection) design, which arise in supervisory control of DEDS. It is shown through an example that a reduced supervisor of minimal size does not necessarily result in a maximal projection when a projection design method which uses the transition structure of a supervisor is applied. Also, if an L-realizable projection P is available and if a supervisor has a special structural feature, a cover C for supervisor reduction can be easily obtained. By investigating the control-compatibility of states of the reduced supervisor based on C, we can also check maximality of P in a simple manner.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.409-422
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• 2002

We investigate the relationship between various generalizations of von Neumann regularity condition and the condition that every prime ideal is maximal in exchange rings.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.773-791
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• 2017

In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.

• Journal of English Language & Literature
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• v.56 no.6
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• pp.1135-1161
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• 2010

The interpretations of degree expressions require the postulation of new entities to represent degrees. Diverse entities such as degrees, intervals, and vectors are adopted for degree expressions. Positive degree sentences and questions are properly construed with the introduction of these entities, but their negative counterparts need more consideration. Negative degree sentences show dual patterns of entailments depending on contexts, and negative degree questions are unacceptable, making weak islands. To explicate the distinct nature of negative degree sentences and questions, Fox & Hackl (2006) provide an analysis based on degrees while Abrusan & Spector (2010) suggest a proposal in interval readings of degree expressions. I have pointed out the theoretical problems of these analyses and proposed an alternative in the framework of the vector space semantics, following Winter (2005). Bi-directional scales in vector space fit well with the dual patterns of negative degree sentences, and the notion of a reference vector is useful to accommodate the contextual influence in negative degree sentences and to deal with the unacceptability of negative degree questions.