• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1193-1200
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• 2013

The center of the Lie group $SU(n)$ is isomorphic to $\mathbb{Z}_n$. If $d$ divides $n$, the quotient $SU(n)/\mathbb{Z}_d$ is also a Lie group. Such groups are locally isomorphic, and their Weyl groups $W(SU(n)/\mathbb{Z}_d)$ are the symmetric group ${\sum}_n$. However, the integral representations of the Weyl groups are not equivalent. Under the mod $p$ reductions, we consider the structure of invariant rings $H^*(BT^{n-1};\mathbb{F}_p)^W$ for $W=W(SU(n)/\mathbb{Z}_d)$. Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non-polynomial cases.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.1-5
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• 2010

Let P be a prime ideal of a commutative unital ring R; X an indeterminate; D := R/P; L the quotient field of D; F an algebraic closure of L; ${\alpha}$ ${\in}$ L[X] a monic irreducible polynomial; ${\xi}$ any root of in F; and Q = ${\alpha}$>, the upper to P with respect to ${\alpha}$. Then R[X]/Q is R-algebra isomorphic to $D[{\xi}]$; and is R-isomorphic to an overring of D if and only if deg(${\alpha}$) = 1.

• Research in Mathematical Education
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• v.15 no.4
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• pp.311-325
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• 2011

In this paper I propose that teaching students the most efficient method of problem solving may curtail students' creativity. Instead it is important to arm students with a variety of problem solving heuristics. It is the students' responsibility to decide which heuristic will solve the problem. The chosen heuristic is the one which is meaningful to the students.

• Research in Mathematical Education
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• v.8 no.3
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• pp.215-226
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• 2004

The purpose of this paper is to introduce an activity of student who found purely linear algebraic solution of the Blackout puzzle. It shows how we can help and work with gifted students. It deals with algorithm, mathematical modeling, optimal solution and software.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.75-95
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• 1999

Dimensions of irreducible $so_5(F)$-modules over an algebraically closed field F of characteristics p > 2 shall be obtained. It turns out that they should be coincident with $p^{m}$, where 2m is the dimension of coadjoint orbits of ${\chi}{\in}so_5(F)^*{\backslash}0$ as Premet asserted. But there is no subregular point for $g=sp_4(F)=so_5(F)$ over F.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.13-22
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• 2019

We compute the second cohomology of the affine Lie algebra aff(1) on the dimensional real space with coefficients in the space ${\mathcal{D}}^n_{{\underline{\lambda}},{\mu}}$ of n-ary linear differential operators acting on weighted densities where ${\underline{\lambda}}=({\lambda}_1,{\ldots},{\lambda}_n)$. We explicitly give 2-cocycles spanning these cohomology.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.209-219
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• 2021

We define a new concept of module amenability which is compatible with original definition of amenability. For a module dual algebra 𝓐, we will show that if every module derivation D : 𝓐** → J𝓐**⊥ is inner then 𝓐 is weak module amenable. Moreover, we will prove that under certain conditions, weak module amenability of 𝓐** implies weak module amenability of 𝓐.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1253-1270
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• 2015

Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if $x_1,{\ldots },x_t$ ($1{\leq}t{\leq}n$) be a sub-set of a system of parameters for M, then the R-module $H^t_{(x_1,{\ldots },x_t)}$(R) is faithful, i.e., Ann $H^t_{(x_1,{\ldots },x_t)}$(R) = 0. Also, it is shown that, if $H^i_I$ (R) = 0 for all i > dim R - dim R/I, then the R-module $H^{dimR-dimR/I}_I(R)$ is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module $H^1_I(M)$, when $H^i_I(M)=0$ for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra $D_I(R)$ is a flat R-algebra.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.397-420
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• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.

• Research in Mathematical Education
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• v.23 no.1
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• pp.13-22
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• 2020

The effectiveness of mathematics classroom teaching is directly affected by the teaching language. Comparing the teaching language of a novice teacher in algebra instruction with an expert teacher from the perspective of pragmatics, it comes to a conclusion that: both teachers attach great importance to the use of the teaching language, with the proportion of the teaching language time more than 50%; the novice teacher uses the affirmative language frequently, twice as often as the expert teacher; the declarative language the novice teacher uses in the exploration is mostly to repeat students' answer, which takes up a short time; the novice teacher uses the teaching language too much in the consolidation, which causes fewer opportunities for students to think. Then we get the following revelations: streamline the teaching language and control the time of the teaching language reasonably; make good use of the affirmative language to provide students hints and necessary time for thinking; avoid simple restatement of the student's answer and use the declarative language ingeniously to improve the feedback quality; use the teaching language appropriately to help students accumulate basic experience in mathematics activities.