• East Asian mathematical journal
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• v.21 no.1
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• pp.9-19
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• 2005

In this paper, some properties of intuitionistic fuzzy o-subalgebras of BCK-algebra with condition(S) are investigated.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.467-474
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• 2002

Let A be C(D), A(D), P(T), C(T), or H$\^$$\infty$/(U). We evaluate the quotient group GL(A) by exp(A).

• East Asian mathematical journal
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• v.27 no.5
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• pp.513-520
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• 2011

In this paper, we introduce the concept of a vague filter of MTL-algebra, and then some related properties are investigated.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.261-266
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• 2017

H. R. Ebrahimi Vishki et al. conjectured in [1], that if every Jordan higher derivation on a trivial generalized matrix algebra $\mathcal{G}=(A,M,N,B)$ is a higher derivation, then either M = 0 or N = 0. In this note, we will give a class of counter examples.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1685-1695
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• 2016

In this article we consider Lie super-bialgebra structures on the generalized loop super-Virasoro algebra ${\mathcal{G}}$. By proving that the first cohomology group $H^1({\mathcal{G}},{\mathcal{G}}{\otimes}{\mathcal{G}})$ is trivial, we obtain that all such Lie bialgebras are triangular coboundary.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1231-1240
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• 2020

The asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field has recently been reviewed. We extend quasi-polynomial behavior of graded Betti numbers of powers of homogenous ideals to ℤ-graded algebra over Noetherian local ring. Furthermore our main result treats the Betti table of filtrations which is finite or integral over the Rees algebra.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1443-1455
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• 2017

Let $M_{z^N}(N{\in}{\mathbb{Z}}^d_+)$ be a bounded multiplication operator on a class of Hilbert spaces with orthogonal basis $\{z^n:n{\in}{\mathbb{Z}}^d_+\}$. In this paper, we prove that each reducing subspace of $M_{z^N}$ is the direct sum of some minimal reducing subspaces. For the case that d = 2, we find all the minimal reducing subspaces of $M_{z^N}$ ($N=(N_1,N_2)$, $N_1{\neq}N_2$) on weighted Bergman space $A^2_{\alpha}({\mathbb{B}}_2)$(${\alpha}$ > -1) and Hardy space $H^2({\mathbb{B}}_2)$, and characterize the structure of ${\mathcal{V}}^{\ast}(z^N)$, the commutant algebra of the von Neumann algebra generated by $M_{z^N}$.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1537-1556
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• 2017

In this paper, we introduce the notion of generating index ${\mathcal{I}}_1(A)$ (2-generating index ${\mathcal{I}}_2(A)$, resp.) of a left-symmetric algebra A, which is the maximum of the dimensions of the subalgebras generated by any element (any two elements, resp.). We give a classification of left-symmetric algebras with ${\mathcal{I}}_1(A)=1$ and ${\mathcal{I}}_2(A)=2$, 3 resp., and show that all such algebras can be constructed by linear and bilinear functions. Such algebras can be regarded as a generalization of those relating to the integrable (generalized) Burgers equation.

• Research in Mathematical Education
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• v.16 no.4
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• pp.217-232
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• 2012

While many studies on early algebra have been conducted, there have been only a few studies on the operation sense as the fundamental element of algebraic thinking, especially the fraction operation sense. This study explored the dimensions of fraction operation sense and then investigated students' fraction operation sense. A total of 183 of sixth graders were surveyed and 5 students who showed high operation sense were clinically interviewed in order to analyze their algebraic thinking in detail. The results showed that students had a tendency to use direct calculation or employ inappropriate operation sense rather than to use the structure of operation or the relation between operations on the basis of algebraic thinking. This study implies that explicit instruction on early algebra is necessary from the elementary school years.

• Research in Mathematical Education
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• v.18 no.2
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• pp.129-148
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• 2014

In this study, we examined the relationships among years of teaching experience, professional rank, number of courses taken, and knowledge of algebra for teaching (KAT). 338 in-service and 376 pre-service secondary mathematics teachers in China completed a KAT questionnaire. Various statistical techniques were employed to examine these relationships. The pre-service participants teachers performed statistically significantly higher in advanced mathematics knowledge than their in-service counterparts. Among the inservice teachers, senior teachers had scored higher in school mathematics and teaching mathematics, compared with junior teachers. Yet participants' advanced mathematics knowledge decreased as their professional rank advanced or their teaching experience increased. The number of courses taken has significantly positive correlation with school mathematics knowledge and advanced mathematics knowledge. The implications of these findings for mathematics teacher education are discussed.