• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.645-651
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• 2012

Based on a sub-BCK-algebra K of a BCI-algebra X, the notions of N-subalgebras and N-ideals of X are introduced, and their relations/properties are investigated.

• Honam Mathematical Journal
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• v.28 no.1
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• pp.57-67
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• 2006

we apply the hyperstructures to BCC-algebras, and introduce the concept of a hyper BCC-algebra which is a generalization of a BCC-algebra, and investigates some related properties. We also introduce the notion of a hyper BCC-subalgebra, BCC-scalar element and a hyper BCC-ideal, and discuss related properties.

• 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 applied mathematics & informatics
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• v.34 no.3_4
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• pp.331-340
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• 2016

The notion of θ-generalized int-soft subalgebras of BE-algebras is introduced, and related properties are investigated. Relations between int-soft subalgebras and θ-generalized int-soft subalgebras are discussed, and characterizations of θ-generalized int-soft subalgebras are considered.

• Korean Journal of Mathematics
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• v.10 no.2
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• pp.97-101
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• 2002

In this paper, we introduce the notion of T-part of BCI-algebras relative to a subset. We show that if A is a subalgebra of a BCI-algebra X, then so is the T-part $T_A(X)$ of X relative to A. We provide equivalent conditions that the T-part of X relative to A is an ideal.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.135-144
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• 2012

falling subalgebra/ideal of a BCK/BCI-algebra is introduced. Relations between falling subalgebras and falling ideals are given. Relations between fuzzy subalgebras/ideals and falling sub-algebras/ideals are provided. A characterization of a falling ideal is established.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.925-932
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• 2008

The notion of weak filters in WFI-algebras is introduced. Relations between weak filters and concrete filters are established. A condition for a filter to be closed is given. Also, a condition for a filter to be a weak filter is provided. Characterizations of weak and concrete filters are discussed. A condition for a subalgebra to be a concrete filter is given.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.15-22
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• 2012

Using $\mathcal{N}$-structures, the notion of an $\mathcal{N}$-essence in a sub-traction algebra is introduced, and related properties are investigated. Relations among an $\mathcal{N}$-ideal, an $\mathcal{N}$-subalgebra and an $\mathcal{N}$-essence are investigated.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.603-611
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• 2016

In this paper, we show that if $\mathcal{A}$ is a differential subalgebra of Banach algebras $\mathcal{B}({\ell}^r)$, $1{\leq}r{\leq}{\infty}$, then solutions of the infinite dimensional linear system associated with a matrix in $\mathcal{A}$ have its p-exponential stability being equivalent to each other for different $1{\leq}p{\leq}{\infty}$.

• 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 $i=1,2$.