• 대한수학회논문집
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• 제15권1호
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• pp.37-44
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• 2000

In this paper, for a given p-adic quasicharacter $c_{v}$ : $k_{v}$longrightarrow $Q_{p}$ satisfying a special condition, we will explicitly construct an admissible pairing corresponding to $c_{v}$. We define a p-adic height on the arbitrary abelian varieties associated to divisors and $c_{v}$ by using admissible pairings at every nonarchimedean places. We also show that our p-adic height satisfies similar properties of Neron-Tate's canonical p-adic height.t.ght.t.t.

• 대한수학회지
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• 제39권5호
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• pp.765-773
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• 2002

Let $textsc{k}$＝$F_{q}$(T) be a rational function field. Let $\ell$ be a prime number with ($\ell$, q-1) ＝ 1. Let K/$textsc{k}$ be an elmentary abelian $\ell$-extension which is contained in some cyclotomic function field. In this paper, we study the $\ell$-divisibility of ideal class number $h_{K}$ of K by using cyclotomic units.s.s.

• 대한수학회보
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• 제47권2호
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• pp.307-317
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• 2010

In this paper we find necessary and sufficient conditions for weak amenability of the convolution Banach algebras A(K) and $L^2(K)$ for a compact hypergroup K, together with their applications to convolution Banach algebras $L^p(K)$ ($2\;{\leq}\;p\;<\;{\infty}$). It will further be shown that the convolution Banach algebra A(G) for a compact group G is weakly amenable if and only if G has a closed abelian subgroup of finite index.

• 대한수학회보
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• 제51권6호
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• pp.1727-1733
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• 2014

The 2-hyperreflexivity of Toeplitz-harmonic type subspace generated by an isometry or a quasinormal operator is shown. The k-hyperreflexivity of the tensor product $\mathcal{S}{\otimes}\mathcal{V}$ of a k-hyperreflexive decom-posable subspace $\mathcal{S}$ and an abelian von Neumann algebra $\mathcal{V}$ is established.

• 대한수학회보
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• 제50권6호
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• pp.1957-1972
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• 2013

The reflexive property for ideals was introduced by Mason and has important roles in noncommutative ring theory. In this note we study the structure of idempotents satisfying the reflexive property and introduce reflexive-idempotents-property (simply, RIP) as a generalization. It is proved that the RIP can go up to polynomial rings, power series rings, and Dorroh extensions. The structure of non-Abelian RIP rings of minimal order (with or without identity) is completely investigated.

• 대한수학회지
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• 제54권1호
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• pp.177-191
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• 2017

In this note we consider the right unit-duo ring property on the powers of elements, and introduce the concept of weakly right unit-duo ring. We investigate first the properties of weakly right unit-duo rings which are useful to the study of related studies. We observe next various kinds of relations and examples of weakly right unit-duo rings which do roles in ring theory.

• 대한수학회보
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• 제41권2호
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• pp.347-357
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• 2004

In this note we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability for the cubic functional equation f(3$\chi$+y) + f($3\chi$-y) = $3f(\chi$+ y) + $3f(\chi$-y) + ($48f(\chi)$ on abelian groups.

• 대한수학회논문집
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• 제25권2호
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• pp.283-289
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• 2010

Approximate fibrations provide a useful class of maps. Fibrators give instant detection of maps in this class, and PL fibrators do the same in the PL category. We show that rational homology spheres with some additional conditions are codimension-k PL fibrators and PL manifolds with trivial homology groups in some range can be codimension-k (k > 2) PL fibrators.

• 대한수학회보
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• 제46권2호
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• pp.295-301
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• 2009

We prove the Hyers-Ulam stability of a Pexiderized exponential equation of mappings f, g, h : $G{\times}S{\rightarrow}{\mathbb{C}}$, where G is an abelian group and S is a commutative semigroup which is divisible by 2. As an application we obtain a stability theorem for Pexiderized exponential equation in Schwartz distributions.

• 대한수학회지
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• 제46권6호
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• pp.1165-1178
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• 2009

In this paper we classify finite groups whose nonnormal subgroups are of order p or pq, where p, q are primes. As a by-product, we also classify the finite groups in which all nonnormal subgroups are cyclic.