• 호남수학학술지
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• 제27권4호
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• pp.571-581
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• 2005

The Weyl-type non-associative algebra ${\overline{WN_{g_n,m,s_r}}$ and its subalgebra ${\overline{WN_{n,m,s_r}}$ are defined and studied in the papers [8], [9], [10], [12]. We will prove that the Weyl-type non-associative algebra ${\overline{WN_{n,0,0_{[2]}}}$ and its corresponding semi-Lie algebra are simple. We find the non-associative algebra automorphism group $Aut_{non}({\overline{WN_{1,0,0_{[2]}}})$.

• 호남수학학술지
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• 제27권4호
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• pp.583-593
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• 2005

The Weyl-type non-associative algebra ${\overline{WN_{g_n,m,s_r}}$ and its subalgebra ${\overline{WN_{n,m,s_r}}$ are defined and studied in the papers [2], [3], [9], [11], [12]. We find the derivation group $Der_{non}({\overline{WN_{1,0,0_{[2]}}})$ the non-associative simple algebra ${\overline{WN_{1,0,0_{[2]}}}$.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.491-500
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• 2006

In this paper, we define intuitionistic fuzzy subalgebras of B-algebras which is related to several classes of algebras such as BCI/BCK-algebras. We could obtain some important results for the homomorphic image and equivalence relations on IFS(X).

• Korean Journal of Mathematics
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• 제8권2호
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• pp.155-162
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• 2000

For a sequence $\{{\eta}_m\}_m$ of unit vectors in $\mathbb{C}^n$, we consider the associated linear functional ${\omega}$ on the Cuntz algebra $\mathcal{O}_n$. We show that the restriction ${\omega}{\mid}_{UHF_n}$ is the product pure state of a subalgebra $UHF_n$ of $\mathcal{O}_n$ such that ${\omega}{\mid}_{UHF_n}={\otimes}{\omega}_m$ with ${\omega}_m({\cdot})$ < ${\cdot}{\eta}_m,{\eta}_m$ >. We study product pure states of UHF and obtain a concrete description of them in terms of unit vectors. We also study states of $UHF_n$ which is the restriction of the linear functionals on $O_n$ associated to a fixed unit vector in $\mathbb{C}^n$.

• 호남수학학술지
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• 제36권4호
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• pp.863-884
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• 2014

In this paper, we introduce a coupled $\mathcal{N}$-structure which is the generalization of $\mathcal{N}$-structure. Using this coupled $\mathcal{N}$-structure, we have applied in a subtraction algebra and have introduced the notion of a coupled $\mathcal{N}$-subalgebra, a coupled $\mathcal{N}$-ideal. Also the characterization of coupled $\mathcal{N}$-ideal is presented.

• 호남수학학술지
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• 제29권2호
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• pp.213-222
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• 2007

A Weyl type algebra is defined in the paper (see [2],[4], [6], [7]). A Weyl type non-associative algebra $\bar{WN_{m,n,s}}$ and its restricted subalgebra $\bar{WN_{m,n,s_r}}$ are defined in the papers (see [1], [14], [16]). Several authors find all the derivations of an associative (Lie or non-associative) algebra (see [3], [1], [5], [7], [10], [16]). We find Der($\bar_{WN_{0,0,1_n}}$) of the algebra $\bar_{WN_{0,0,1_n}}$ and show that the algebras $\bar_{WN_{0,0,1_n}}$ and $\bar_{WN_{0,0,s_1}}$ are not isomorphic in this work. We show that the associator of $\bar_{WN_{0,0,1_n}}$ is zero.

• 대한수학회지
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• 제46권3호
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• pp.657-673
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• 2009

The fixed point algebra $C^*(E)^{\gamma}$ of a gauge action $\gamma$ on a graph $C^*$-algebra $C^*(E)$ and its AF subalgebras $C^*(E)^{\gamma}_{\upsilon}$ associated to each vertex v do play an important role for the study of dynamical properties of $C^*(E)$. In this paper, we consider the stability of $C^*(E)^{\gamma}$ (an AF algebra is either stable or equipped with a (nonzero bounded) trace). It is known that $C^*(E)^{\gamma}$ is stably isomorphic to a graph $C^*$-algebra $C^*(E_{\mathbb{Z}}\;{\times}\;E)$ which we observe being stable. We first give an explicit isomorphism from $C^*(E)^{\gamma}$ to a full hereditary $C^*$-subalgebra of $C^*(E_{\mathbb{N}}\;{\times}\;E)({\subset}\;C^*(E_{\mathbb{Z}}\;{\times}\;E))$ and then show that $C^*(E_{\mathbb{N}}\;{\times}\;E)$ is stable whenever $C^*(E)^{\gamma}$ is so. Thus $C^*(E)^{\gamma}$ cannot be stable if $C^*(E_{\mathbb{N}}\;{\times}\;E)$ admits a trace. It is shown that this is the case if the vertex matrix of E has an eigenvector with an eigenvalue $\lambda$ > 1. The AF algebras $C^*(E)^{\gamma}_{\upsilon}$ are shown to be nonstable whenever E is irreducible. Several examples are discussed.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.549-555
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• 2006

Using a t-norm, the notion of T-fuzzy subalgebras of right K(G)-algebras is introduced, and fundamental properties are investigated. The fact that T-fuzzy subalgebras of a right K(G)-algebra form a complete lattice is proved.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.453-459
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• 2004

A left-invariant flat Riemannian connection on a Lie group makes its Lie algebra a left symmetric algebra compatible with an inner product. The left symmetric algebra is decomposed into trivial ideal and a subalgebra of e(l). Using this result, the Lie group is embedded isomorphically into the direct product of O(l) $\times$ $R^{k}$ for some nonnegative integers l and k.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.429-442
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• 2023

In this paper, we introduce the concept of fuzzy ideals, anti-fuzzy ideals of Γ-BCK-algebras. We study the properties of fuzzy ideals, anti-fuzzy ideals of Γ-BCK-algebras. We prove that if f^-1(µ) is a fuzzy ideal of M, then µ is a fuzzy ideal of N, where f : M → N is an epimorphism of Γ-BCK-algebras M and N.