• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.249-254
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• 2000

We give an easy proof of the fact that every noncommutative torus $A_{\omega}$ is stably isomorphic to the noncommutative torus $C(\widehat{S\omega}){\;}\bigotimes{\;}A_p$ which hasa trivial bundle structure. It is well known that stable isomorphism of two separable $C^{*}-algebras$ is equibalent to the existence of eqivalence bimodule between the two stably isomorphic $C^{*}-algebras{\;}A_{\omega}$ and $C(\widehat{S\omega}){\;}\bigotimes{\;}A_p$.

• The Mathematical Education
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• v.25 no.3
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• pp.57-69
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• 1987

A geometric interpretation of t-designs, in the context of posets, is given in the association scheme, not isomorphic with the Hamming scheme H(2,4), but having the same parameters as H(2,4). It is also shown that there is no similar poset which characterizes the designs for ally of the three exceptional association schemes, not isomorphic with the Johnson scheme J(8,2), but having the same parameters as J(8,2).

• 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.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.1-14
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• 2024

Recently, Zhao, Wang, and Pu introduced and studied new concepts of nonnil-commutative diagrams and nonnil-projective modules. They proved that an R-module that is nonnil-isomorphic to a projective module is nonnil-projective, and they proposed the following problem: Is every nonnil-projective module nonnil-isomorphic to some projective module? In this paper, we delve into some new properties of nonnil-commutative diagrams and answer this problem in the affirmative.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.331-340
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• 1998

We define the spherical non-commutative torus $L_{\omega}$/ as the crossed product obtained by an iteration of l crossed products by actions of, the first action on C( $S^{2n＋l}$). Assume the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus $A_{p}$ with a matrix algebra $M_{m}$ ( ) (m > 1). We prove that $L_{\omega}$/ $M_{p}$ (C) is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{mp}$ (C), and that the tensor product of $L_{\omega}$/ with a UHF-algebra $M_{p{\infty}}$ of type $p^{\infty}$ is isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) $M_{p{\infty}}$ if and only if the set of prime factors of m is a subset of the set of prime factors of p. Furthermore, it is shown that the tensor product of $L_{\omega}$/, with the C＊-algebra K(H) of compact operators on a separable Hilbert space H is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) K(H) if Prim( $L_{\omega}$/) is homeomorphic to $L^{k}$ (n)$\times$ $T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.$T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.e.

• Bulletin of the Korean Chemical Society
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• v.26 no.12
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• pp.2072-2074
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• 2005

• Communications of the Korean Mathematical Society
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• v.8 no.3
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• pp.361-371
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• 1993

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.151-167
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• 2007

If k is a subfield of $\mathbb{Q}(\varepsilon_m)$ then the cohomology group $H^2(k(\varepsilon_n)/k)$ is isomorphic to $H^2(k(\varepsilon_{n'})/k)$ with gcd(m, n') = 1. This enables us to reduce a cyclotomic k-algebra over $k(\varepsilon_n)$ to the one over $k(\varepsilon_{n'})$. A radical extension in projective Schur algebra theory is regarded as an analog of cyclotomic extension in Schur algebra theory. We will study a reduction of cohomology group of radical extension and show that a Galois cohomology group of a radical extension is isomorphic to that of a certain subextension of radical extension. We then draw a cohomological characterization of radical group.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.609-618
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• 1994

F. Rhodes [2] introduced the fundamental group $\sigma(X, x_0, G)$ of a transformation group (X,G) as a generalization of the fundamental group $\pi_1(X, x_0)$ of a topological space X and showed a sufficient condition for $\sigma(X, x_0, G)$ to be isomorphic to $\pi_1(X, x_0) \times G$, that is, if (G,G) admits a family of preferred paths at e, $\sigma(X, x_0, G)$ is isomorphic to $\pi_1(X, x_0) \times G$. B.J.Jiang [1] introduced the Jiang subgroup $J(f, x_0)$ of the fundamental group of X which depends on f and showed a condition to be $J(f, x_0)$ = Z(f_\pi(\pi_1(X, x_0)), \pi_1(X, f(x_0)))$.

• 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.