• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.241-250
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• 2003

Let (B, m$_{B}$, k) be a maximal commutative $textsc{k}$-subalgebra of M$_{m}$(k). Then, for some element z $\in$ Soc(B), a k-algebra R = B［X,Y］/I, where I ＝ (m$_{B}$X, m$_{B}$Y, X$^2$- z,Y$^2$- z, XY) will create an interesting maximal commutative $textsc{k}$-subalgebra of a matrix algebra which is neither a $C_1$-construction nor a $C_2$-construction. This construction will also be useful to embed a maximal commutative $textsc{k}$-subalgebra of matrix algebra to a maximal commutative $textsc{k}$-subalgebra of a larger size matrix algebra.gebra.a.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.147-153
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• 2009

In this paper, we give some constructions of implicative/commutative d-algebras which are not BCK-algebras. This demonstrate that the notion of implicative/commutative d-algebras are indeed generalizations of the same in BCK-algebras.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.73-84
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• 2008

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to commutative ideals in BCK-algebras. The notion of an intuitionistic fuzzy commutative ideal of a BCK-algebra is introduced, and some related properties are investigated. Characterizations of an intuitionistic fuzzy commutative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy commutative ideal are given. Using a collection of commutative ideals, intuitionistic fuzzy commutative ideals are established.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.23-32
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• 2004

Let (B, $m_B$, ${\kappa}$) be a maximal commutative ${\kappa}$-subalgebra of a matrix algebra $M_n(\kappa)$. We will construct a maximal commutative ${\kappa}$-subalgebra (R, $m$, ${\kappa}$) of $M_n+3(\kappa)$ from the algebra B such that the algebra R has dimension greater than the dimension of B by 3. Moreover, we will show a $C_i$-construction doesn't imply a $C^3_2$-construction for $i=1,2$.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.331-340
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• 1998

We define the spherical non-commutative torus $L_{\omega}$/ as the crossed product obtained by an iteration of l crossed products by actions of, the first action on C( $S^{2n＋l}$). Assume the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus $A_{p}$ with a matrix algebra $M_{m}$ ( ) (m > 1). We prove that $L_{\omega}$/ $M_{p}$ (C) is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{mp}$ (C), and that the tensor product of $L_{\omega}$/ with a UHF-algebra $M_{p{\infty}}$ of type $p^{\infty}$ is isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) $M_{p{\infty}}$ if and only if the set of prime factors of m is a subset of the set of prime factors of p. Furthermore, it is shown that the tensor product of $L_{\omega}$/, with the C＊-algebra K(H) of compact operators on a separable Hilbert space H is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) K(H) if Prim( $L_{\omega}$/) is homeomorphic to $L^{k}$ (n)$\times$ $T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.$T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.e.

• The Pure and Applied Mathematics
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• v.18 no.1
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• pp.41-50
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• 2011

Based on the theory of falling shadows and fuzzy sets, the notion of a falling fuzzy commutative ideal of a BCK-algebra is introduced. Relations between falling fuzzy commutative ideals and falling fuzzy ideals are investigated.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.13-26
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• 1998

The purpose of this note is to study the relation between Heyting algebra and t-algebra which is the dual concept of BCK-algebra. We define t-algebra with binary operation ${\rhd}$ which is a generalization of the implication in the Heyting algebra, and define a bounded ness and commutativity of it, and then characterize a Heyting algebra and a Boolean algebra as a bounded commutative t-algebra X satisfying $x=(x{\rhd}y){\rhd}x$ for all $x,y{\in}X$.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.1-11
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• 2000

The non-commutative torus $A_{\omega}=C^*(\mathbb{Z}^n,{\omega})$ may be realized as the $C^*$-algebra of sections of a locally trivial $C^*$-algebra bundle over $\widehat{S_{\omega}}$ with fibres $C^*(\mathbb{Z}^n/S_{\omega},{\omega}_1)$ for some totally skew multiplier ${\omega}_1$ on $\mathbb{Z}^n/S_{\omega}$. It is shown that $A_{\omega}{\otimes}M_l(\mathbb{C})$ has the trivial bundle structure if and only if $\mathbb{Z}^n/S_{\omega}$ is torsion-free.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.15-21
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• 1999

In this paper, we introduce the notion of anti fuzzy prime ideals in a commutative BCK-algebra and obtain some properties of it.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.399-404
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• 2005

Let M be a finite commutative nilpotent algebra over a perfect field k of prime characteristic p and let $M^p$ be the sub-algebra of M generated by $x^p$, $x{\in}M$. Eggert[3] conjectures that $dim_kM{\geq}pdim_kM^p$. In this paper, we show that the conjecture holds for $M=R^+/I$, where $R=k[X_1,\;X_2,\;{\cdots},\;X_t]$ is a polynomial ring with indeterminates $X_1,\;X_2,\;{\cdots},\;X_t$ over k and $R^+$ is the maximal ideal of R generated by $X_1,\;X_2,{\cdots},\;X_t$ and I is a monomial ideal of R containing $X_1^{n_1+1},\;X_2^{n_2+1},\;{\cdots},\;X_t^{n_t+1}$ ($n_i{\geq}0$ for all i).