• Honam Mathematical Journal
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• v.33 no.1
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• pp.93-113
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• 2011

Let $a{\oplus}b$ = max(a, b), $a{\otimes}b$=a+b, a, $b\in\mathbb{R}_{\varepsilon}\;:=\cup\{-\infty\}$. In max-plus algebra we work on the linear algebra structure for the pair of operations (${\oplus},{\otimes}$) extended to matrices and vectors over $\mathbb{R}_{\varepsilon}$. In this paper our main aim is to reproduce the work of R. A. Cuninghame-Green [3] on the linear systems over a max-plus semi-field $\mathbb{R}_{\varepsilon}$.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.515-523
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• 2010

In this paper, we introduced a special set, called T-part, in a Q-algebra X. We also show that the T-part of X is a subalgebra of X. By using T-part, we provide an equivalent condition that every ideal is a T-ideal.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.335-349
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• 2009

Soft set theory by Molodtsov is applied to ideals in BCC-algebras. The notion of soft BCC-ideals of soft BCC-algebras and idealistic soft BCC-algebras are introduced, and several examples are provided. Relations between a fuzzy BCC-ideal and an idealistic soft BCC-algebra are given, and the characterization of idealistic soft BCC-algebras is established.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.379-390
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• 2008

More general forms of a BZ-ideal and a T-ideal are given, and appropriate examples are provided. The notion of T(m)-type BZ-algebra is introduced, and its characterizations are given.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.227-236
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• 2014

In this paper, we introduce the notion of a generalized derivation in a BE-algebra, and consider the properties of generalized derivations. Also, we characterize the fixed set $Fix_d(X)$ and Kerd by generalized derivations. Moreover, we prove that if d is a generalized derivation of a BE-algebra, every filter F is a d-invariant.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.613-629
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• 2016

In this paper, we introduced the notion of multiplier of Boolean algebras and discuss related properties between multipliers and special mappings, like dual closures, homomorphisms on B. We introduce the notions of xed set $Fix_f(X)$ and normal ideal and obtain interconnection between multipliers and $Fix_f(B)$. Also, we introduce the special multiplier ${\alpha}_p$a nd study some properties. Finally, we show that if B is a Boolean algebra, then the set of all multipliers of B is also a Boolean algebra.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.167-178
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• 2014

In this paper, we introduce the notion of derivation in a BE-algebra, and consider the properties of derivations. Also, we characterize the fixed set $Fix_d(X)$ and Kerd by derivations. Moreover, we prove that if d is a derivation of BE-algebra, every filter F is a d-invariant.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.127-138
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• 2015

In this paper, we introduce the notion of f-derivation in a BE-algebra, and consider the properties of f-derivations. Also, we characterize the fixed set $Fix_d(X)$ and Kerd by f-derivations. Moreover, we prove that if d is a f-derivation of a BE-algebra, every f-filter F is a a d-invariant.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.635-647
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• 1995

Let $H$ denote a separable, infinite dimensional complex Hilbert space and let $L(H)$ denote the algebra of all bounded linear operators on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $1_H$ and is closed in the $weak^*$ operator topology on $L(H)$. For $T \in L(H)$, let $A_T$ denote the smallest subalgebra of $L(H)$ that contains T and $1_H$ and is closed in the $weak^*$ operator topology.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.2
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• pp.182-186
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• 2002

We investigate the quotient structure of a product BCK-algebra and fundamental homomorphism theorem and show their some properties.