• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.77-85
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• 2001

If an Azumaya algebra A is a homomorphic image of a finite group ring RG where G is a direct product of subgroups then A can be decomposed into subalgebras A(sub)i which are homomorphic images of subgroup rings of RG. This result is extended to projective Schur algebras, and in this case behaviors of 2-cocycles will play major role. Moreover considering the situation that A is represented by Azumaya group ring RG, we study relationships between the representing groups for A and A(sub)i.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.789-803
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• 2017

Let $K={\mathbb{Q}}({\alpha})$ be a cubic field where ${\alpha}$ is an algebraic integer such that $disc_K({\alpha})$ is square-free. In this paper we will classify the structure of the unit group of the quotient ring ${\mathcal{O}}_K/A$ for each non-zero ideal A of ${\mathcal{O}}_K$.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.597-603
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• 2000

Let K be an algebraically closed filed of characteristic 0 and let G = Z(sub)m x Z(sub)n. We find the conditions under which the elements of the group ring KG are units and idempotents respectively by using the represented matrix. We can see that if $\alpha$ = ∑r(g)g $\in$ KG is an idempotent then r(1) = 0, 1/mn, 2/mn, …, (mn-1)/mn or 1.

• East Asian mathematical journal
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• v.38 no.5
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• pp.583-591
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• 2022

Let K be an imaginary quadratic field and 𝒪 be an order in K. Let H_𝒪 be the ring class field of 𝒪. Furthermore, for a positive integer N, let K_𝒪,N be the ray class field modulo N𝒪 of 𝒪. When the discriminant of 𝒪 is different from -3 and -4, we construct an extended form class group which is isomorphic to the Galois group Gal(K_𝒪,N/H_𝒪) and describe its Galois action on K_𝒪,N in a concrete way.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.101-103
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• 2008

The structure of $I_G^n/I_G^{n+1}$ for finite abelian group G is investigated.

• Journal of Microbiology and Biotechnology
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• v.15 no.6
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• pp.1280-1285
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• 2005

Using the nodY::lacZ fusion system in Bradyrhizobium japonicum USDA 110, 22 flavonoids, which have structurally different features, were tested to define the role of the substituted functional groups as an inducer or inhibitor for the nod gene expression. A functional ,group of 4'-OH on the B-ring and the double bond between 2-C and 3-C on the C ring were required to induce the nod gene expression in B. japonicum USDA 110. In the case of isoflavones, the 4'-methoxyl group, which blocks the open 4'-OH functional group, did not significantly lower inducing activity, as compared with isoflavones with 4'-OH. However, all flavonols tested, which have a 3-OH functional group on the C-ring, did not induce, but inhibited the nod gene expression. Flavone, 7-hydroxyflavone, and kaempferol (5,7,4'-trihydroxyflavonol) at $1\;{\mu}M$ concentration significantly inhibited the nod gene expression induced by 7,4'-dihydroxyflavone. However, 7-hydroxy-4'-methoxyflavone at $1\;{\mu}M$ concentration showed a synergistic effect with genistein and 7,4'-dihydroxyflavone on the induction activity.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.63-70
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• 1996

Let K be a field of characteristic 0 and G a Klein's four group. We find the idempotent elements and units of the group ring KG by using the basic group table matrix of G.

• Korean Journal of Ichthyology
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• v.12 no.3
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• pp.166-172
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• 2000

Growth of Ammodytes personatus was investigated based on the specimens collected in the costal waters of Shinsudo, Sacheon from March 20 to December 14, 1988. Age determination based on otolith. The rings in the otolith were used as the basis for age annulus. The time of ring formation was estimated to one time per year in May far 1st ring group and March for 2nd ring group. The spawning season peaked in December. It takes approximately 16 months for the first ring and 11 months for the second ring to form in the otolith. The opaque zone was formed and marked over summer at 1st ring group and spawning mark at 2nd ring group. The relationship between the total length(TL) and otolith radius(R), and body weight(BW) were represented respectively as follows: TL=29.17+182.9R, BW=$4.9{\times}10^{-8}TL^{3.9587}$. Von Bertalanffy growth model is $TL_t$ = 177.273 ($1_e^{-0.040(t+7.332)}$), Robertson growth model is $TL_t=\frac{150.275}{1+2.085e^{-0.099t}}$ and Gompertz growth model is $TL_t=157.551e^{-1.214exp(-0.069t)}$.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.301-309
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• 2011

Let R = $Mat_2(F)$ be the ring of all 2 by 2 matrices over a finite field F, X the set of all nonzero, nonunits of R and G the group of all units of R. After investigating some properties of orbits under the left (and right) regular action on X by G, we show that the graph automorphisms group of $\Gamma(R)$ (the zero-divisor graph of R) is isomorphic to the symmetric group $S_{|F|+1}$ of degree |F|+1.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1105-1112
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• 2016

Describing the group of units $U({\mathbb{Z}}G)$ of the integral group ring ${\mathbb{Z}}G$, for a finite group G, is a classical and open problem. In this note, we show that $$U_1({\mathbb{Z}}[T{\times}C_2]){\sim_=}[F_{97}{\rtimes}F_5]{\rtimes}[T{\times}C_2]$$, where $T={\langle}a,b:a^6=1,a^3=b^2,ba=a^5b{\rangle}$ and $F_{97}$, $F_5$ are free groups of ranks 97 and 5, respectively.