• 대한수학회지
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• 제49권1호
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• pp.1-16
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• 2012

In the present paper we describe a class of Gorenstein, finite and at morphism ${\varrho}$: $X{\rightarrow}Y$ of degree 6 of algebraic varieties, called Anglo-American covers. We prove a general Bertini theorem for them and we give some evidence that the cover ${\varrho}$: $A{\rightarrow}\mathbb{P}_k^2$ associated general (1, 3)-polarized abelian surface is Anglo-American.

• Kyungpook Mathematical Journal
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• 제18권1호
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• pp.71-78
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• 1978

Consider the following commutative square of-categories and functors where T and U are (regular epi. monosource) topological and fibre small. G is algebraic and the following two conditions hold: (i) if h: $UA{\rightarrow}UB$ and g: $VA{\rightarrow}VB$ are morphisms such that Gh=Tg. there exists a morphism f: $A{\rightarrow}B$ such that Uf=h and Vf=g; (ii) U-initial monosources are carried into T-initial monosources by V.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권1호
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• pp.25-29
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• 1995

The topos constructed in [6] is a set-like category that includes among its axioms an axiom of infinity and an axiom of choice. In its final form a topos is free from any such axioms. Set$\^$G/ is a topos whose object are G-set Ψ$\sub$s/:G${\times}$S\longrightarrowS and morphism f:S \longrightarrowT is an equivariants map. We already known that Set$\^$G/ satisfies the weak form of the axiom of choice but it does not satisfies the axiom of the choice.(omitted)

• 호남수학학술지
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• 제20권1호
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• pp.121-133
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• 1998

We find some properties of the pro-torsion products. Under the suitable conditions, we also show that the map ${\bar{H}}_P({\chi};G){\rightarrow}{\bar{H}}_p^{s(r)}({\chi};G)$ is an isomorphism and the n-th homotopy group of X is isomorphic to the n-th ${\check{C}}ECH$ homology group.

• 충청수학회지
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• 제24권3호
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• pp.427-436
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• 2011

In this paper, we first show that the pull-back morphism between two K-groups of the Steinberg varieties, obtained respectively from partial flag varieties and quiver varieties of type A, is a ring homomorphism with respect to the convolution product. Then, we prove that this ring homomorphism yields a property of compatibility between two certain convolution actions.

• 대한수학회보
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• 제49권2호
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• pp.307-317
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• 2012

We say (W, {${\phi}_1,\;{\ldots}\;,{\phi}_t$}) is a polarizable dynamical system of several morphisms if ${\phi}_i$ are endomorphisms on a projective variety W such that ${\otimes}{\phi}_i^*L$ is linearly equivalent to $L^{{\otimes}q}$ for some ample line bundle L on W and for some q > t. If q is a rational number, then we have the equidistribution of small points of given dynamical system because of Yuan's work [13]. As its application, we can build a polarizable dynamical system of an automorphism and its inverse on a K3 surface and can show that its periodic points are equidistributed.

• 대한수학회보
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• 제55권4호
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• pp.1023-1035
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• 2018

We strengthen a result of Michiel Kosters by proving the following theorems: (*) Let ${\phi}:W{\rightarrow}V$ be a finite surjective morphism of algebraic varieties over an ample field K. Suppose V has a simple K-rational point a such that $a{\not\in}{\phi}(W(K_{ins}))$. Then, card($V(K){\backslash}{\phi}(W(K))$ = card(K). (**) Let K be an infinite field of positive characteristic and let $f{\in}K[X]$ be a non-constant monic polynomial. Suppose all zeros of f in $\tilde{K}$ belong to $K_{ins}{\backslash}K$. Then, card(K \ f(K)) = card(K).

• 대한수학회보
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• 제54권6호
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• pp.1991-1999
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• 2017

Let A and B be two Banach algebras and $T:B{\rightarrow}A$ be a bounded homomorphism, with ${\parallel}T{\parallel}{\leq}1$. Recently, Dabhi, Jabbari and Haghnejad Azar (Acta Math. Sin. (Engl. Ser.) 31 (2015), no. 9, 1461-1474) obtained some results about the n-weak amenability of $A{\times}_TB$. In the present paper, we address a gap in the proof of these results and extend and improve them by discussing general necessary and sufficient conditions for $A{\times}_TB$ to be n-weakly amenable, for an integer $n{\geq}0$.

• 대한수학회지
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• 제55권4호
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• pp.809-832
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• 2018

In this paper, we form the basis of the abstract theory for constructing the $K{\ddot{u}}nneth$ spectral sequence for a complex of Banach spaces. As the category of Banach spaces is not abelian, several difficulties occur and hinder us from applying the usual method of homological algebra directly. The most notable facts are the image of a morphism of Banach spaces is not necessarily a Banach space, and also the closed summand of a Banach space need not be a topological direct summand. So, we consider some conditions and categorical terms that fit the category of Banach spaces to modify the familiar method of homological algebra.

• 대한수학회보
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• 제40권1호
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• pp.29-51
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• 2003

In this paper we construct a natural filtration associated to the plethysm $S_{r}(\wedge^2 \varphi)$ over arbitrary commutative ring R. Let $\phi$ : G longrightarrow F be a morphism of finite free R-modules. We construct the natural filtration of $S_{r}(\wedge^2 \varphi)$ as a $GL(F){\times}GL(G)$- complex such that its associated graded complex is ${\Sigma}_{{\lambda}{\in}{\Omega}_{\gamma}}=L_{2{\lambda}{\varphi}$, where ${{\Omega}_{\gamma}}^{-}$ is a set of partitions such that $│\wedge│\;=;{\gamma}\;and\;2{\wedge}$ is a partition of which i-th term is $2{\wedge}_{i}$. Specializing our result, we obtain the filtrations of $S_{r}(\wedge^2 F)\;and\;D_{r}(D_2G).