• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.441-451
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• 2019

In this paper, we introduce the notion of symmetric bi-f-derivation on subtraction algebra and investigated some related properties. Also, we prove that if D : X → X is a symmetric bi-f-derivation on X, then D satisfies D(x - y, z) = D(x, z) - f(y) for all x, y, z ∈ X.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.387-393
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• 2021

In this paper, we introduce the notion of symmetric bi-derivations on subtraction algebra and investigated some related properties. We prove that a map D : X × X → X is a symmetric bi-derivation on X if and only if D is a symmetric map and it satisfies D(x - y, z) = D(x, z) - y for all x, y, z ∈ X.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.259-267
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• 2002

Let X be a hemicompact space with ($K_{n}$) as an admissible exhaustion, and for each n $\in$ N, $A_{n}$ a Banach function algebra on $K_{n}$ with respect to $\parallel.\parallel_n$ such that $A_{n+1}\midK_{n}$$\subsetA_n$ and${\parallel}f{\mid}K_n{\parallel}_n{\leq}{\parallel}f{\parallel}_{n+1}$ for all f$\in$$A_{n+1}$, We consider the subalgebra A = { f $\in$ C(X) : $\forall_n\;{\epsilon}\;\mathbb{N}$ of C(X) as a frechet function algebra and give a result related to its spectrum when each $A_{n}$ is natural. We also show that if X is moreover noncompact, then any closed subalgebra of A cannot be topologized as a regular Frechet Q-algebra. As an application, the Lipschitzalgebra of infinitely differentiable functions is considered.d.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.257-267
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• 2000

In this article, we investigate positive interpolation problems in tridiagonal algebra which was introduded by F. Gilfeather and D. Larson.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.73-82
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• 2022

Let K be a field of characteristic zero. We first show that images of the linear derivations and the linear 𝓔-derivations of the polynomial algebra K[x] = K[x₁, x₂, …, x_n] are ideals if the products of any power of eigenvalues of the matrices according to the linear derivations and the linear 𝓔-derivations are not unity. In addition, we prove that the images of D and 𝛿 are Mathieu-Zhao spaces of the polynomial algebra K[x] if D = ∑ⁿ_i=1 (a_ix_i + b_i)∂_i and 𝛿 = I - 𝜙, 𝜙(x_i) = λ_ix_i + 𝜇_i for a_i, b_i, λ_i, 𝜇_i ∈ K for 1 ≤ i ≤ n. Finally, we prove that the image of an affine 𝓔-derivation of the polynomial algebra K[x₁, x₂] is a Mathieu-Zhao space of the polynomial algebra K[x₁, x₂]. Hence we give an affirmative answer to the LFED Conjecture for the affine 𝓔-derivations of the polynomial algebra K[x₁, x₂].

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1159-1180
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• 2019

In this article, we present the notion of e-fuzzy filters in an MS-Algebra and characterize in terms of equivalent conditions. The concept of D-fuzzy filters is studied and the set of equivalent conditions under which every e-fuzzy filter is an D-fuzzy filter are observed. Moreover we study some properties of the space of all prime e-fuzzy filters of an MS-algebra.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.499-501
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• 1994

Let ${X_n}$ be conditionally i.i.d. given $g \subset \sigma(X_n, n \geq 1)$. We will prove that $g$ is degenerate if and only if ${X_n, n \geq 1}$ are i.i.d. random variable(r.v.s). As a corollary the Hewitt-Savage zero-one law is obtained using the fact that interchageable process is conditionally i.i.d. given the $\sigma$-algebra of permutable events.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.245-252
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• 2002

In this paper we obtain some results concerning Jordan derivations and Jordan left derivations mapping into the Jacobson radical. Our main result is the following : Let d be a Jordan derivation (resp. Jordan left derivation) of a complex Banach algebra A. If d$^2$(x) = 0 for all x $\in$ A, then we have d(A) ⊆ red(A)

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.115-121
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• 1998

The purpose of this paper is to prove the following result: Let A be a noncom mutative Banach algebra. Suppose that there exist continuous linear Jordan derivations $D:A{\rightarrow}A$, $G:A{\rightarrow}A$ such that [$D^2(x)+G(x)$, $x^n$] lies in the Jacobson radical of A for all $x{\in}A$. Then $D(A){\subset}rad(A)$ and $G(A){\subset}rad(A)$.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.53-67
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• 2019

The notions of closed elements and dense elements are introduced in BE-algebras. Characterization theorems of closed elements and closed filters are obtained. The notion of dense elements is introduced in BE-algebras. Dense BE-algebras are characterized with the help of maximal filters and congruences. The concept of D-filters is introduced in BE-algebras. A set of equivalent conditions is derived for every D-filter to become a closed filter.