• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.451-460
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• 2016

The notion of a rough fuzzy filter in a BE-algebra is introduced and some properties of such a filter are investigated. The relations between the upper (lower) rough filters and the upper (lower) approximations of their homomorphism images are discussed.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.933-950
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• 2010

We study a relationship between sets of uniqueness, weakly sufficient sets and sampling sets in the space $A^{-{\infty}}(\mathbb{B})$ of holomorphic functions with polynomial growth on the unit ball of $\mathbb{C}^n$ ($n\;{\geq}\;1$).

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.313-329
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• 2008

In this paper, we study duality in the absolute Schur algebras that were first introduced in [1] and extended in [5]. This is done in a way analogous to the classical Schatten's Theorem on the Banach space $B(l_2)$ of bounded linear operators on $l_2$ involving the duality relation among the class of compact operators K, the trace class $C_1$ and $B(l_2)$. We also study the reflexivity in such the algebras.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.501-509
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• 2013

In this paper we give a definition of the Hodge type Laplacian ${\Delta}$ on a non-commutative manifold which is the smooth dense subalgebra of a $C^*$-algebra. We prove that the Laplacian on a quantum Heisenberg manifold is an elliptic operator in the sense that $({\Delta}+1)^{-1}$ is compact.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.251-258
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• 2015

Let $\mathcal{A}$ be a unital $C^*$-algebra, a, x and y are elements in $\mathcal{A}$. In this paper, we present the expression of the Moore-Penrose inverse and the group inverse of a-$xy^*$ under the conditions $x=aa^+x,y^*=y^*a^+a$, respectively.

• Research in Mathematical Education
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• v.1 no.1
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• pp.1-5
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• 1997

We discuss some aspects of mathematics for teachers such as algebra for teachers, geometry for teachers, statistics for teachers, etc., which can be taught in teacher preparation courses. Mathematics for teachers should consider the followings: (a) Various solutions for a problem, (b) The dynamics of a problem introduced by change of condition, (c) Relationship of mathematics to real life, (d) Mathematics history and historical issues, (e) The difference between pure mathematics and pedagogical mathematics, (f) Understanding of the theoretical backgrounds, and (g) Understanding advanced mathematics.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.25-32
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• 1994

Let A be a (complex) Banach algebra. The object of the this paper shall be remove the continuity of the derivation in the recently theorems. We prove that every derivation D on A satisfying [D(a), a] ${\in}$ Prad(A) for all a ${\in}$ A maps into the radical of A. Also if ${\alpha}D^3+D^2$ is a derivation for some ${\alpha}{\in}C$ and all minimal prime ideals are closed, then D maps into its radical.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.381-387
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• 2002

Our main goal is to show that if there Jordan derivation D, G on a noncommutative (n+1)!-torsion free prime ring R such that D($\chi$)$\chi$$^n$+$\chi$$^n$G($\chi$) $\in$ C(R) for all $\chi$ $\in$ R, then we have D=0 and G=0.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.837-846
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• 1994

Let A denote a unital normed algebra over a field K = R or C and let e be the identity of A. Given $a \in A$ and $x \in A$ with $\Vert x \Vert = 1$, let $$ V(A, a, x) = {f(ax) : f \in A', f(x) = 1 = \Vert f \Vert}. $$ Then the (Bonsall and Duncan) numerical range of an element $a \in A$ is defined by $$ V(a) = \cup{V(A, a, x) : x \in A, \Vert x \Vert = 1}, $$ where A' denotes the dual of A. In [2], $V(a) = {f(a) : f \in A', f(e) = 1 = \Vert f \Vert}$.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.701-718
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• 2019

In this paper we compute the U-projective resolution of kQ-modules where Q is quiver of type $A_n$ and ${\tilde{A}}_n$. The behavior of the sequence can be seen through its geometric representation.