• Title/Summary/Keyword: subalgebra

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INTERVAL-VALUED FUZZY BG-ALGEBRAS

  • Saeid, Arsham Borumand
    • Korean Journal of Mathematics
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    • v.14 no.2
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    • pp.203-215
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    • 2006
  • In this note the notion of interval-valued fuzzy BG-algebras (briefly, i-v fuzzy BG-algebras), the level and strong level BG-subalgebra is introduced. Then we state and prove some theorems which determine the relationship between these notions and BG-subalgebras. The images and inverse images of i-v fuzzy BG-subalgebras are defined, and how the homomorphic images and inverse images of i-v fuzzy BG-subalgebra becomes i-v fuzzy BG-algebras are studied.

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FUZZY ε-SUBALGEBRAS (IDEALS) IN BCI-ALGEBRAS

  • Jun, Young Bae;Lee, Kyoung Ja
    • Journal of the Chungcheong Mathematical Society
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    • v.33 no.4
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    • pp.395-404
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    • 2020
  • Based on a sub-BCK-algebra K of a BCI-algebra X, the notions of fuzzy (K, ε)-subalgebras, fuzzy (K, ε)-ideals and fuzzy commutative (K, ε)-ideals are introduced, and their relations/properties are investigated. Conditions for a fuzzy subalgebra/ideal to be a fuzzy (K, ε)-subalgebra/ideal are provided.

ℵ-IDEALS OF BCK/BCI-ALGERBAS

  • Jun, Young Bae;Lee, Kyoung Ja;Song, Seok Zun
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.417-437
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    • 2009
  • The notions of $\mathcal{N}$-subalgebras, (closed, commutative, retrenched) $\mathcal{N}$-ideals, $\theta$-negative functions, and $\alpha$-translations are introduced, and related properties are investigated. Characterizations of an $\mathcal{N}$-subalgebra and a (commutative) $\mathcal{N}$-ideal are given. Relations between an $\mathcal{N}$-subalgebra, an $\mathcal{N}$-ideal and commutative $\mathcal{N}$-ideal are discussed. We verify that every $\alpha$-translation of an $\mathcal{N}$-subalgebra (resp. $\mathcal{N}$-ideal) is a retrenched $\mathcal{N}$-subalgebra (resp. retrenched $\mathcal{N}$-ideal).

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A CONSTRUCTION OF MAXIMAL COMMUTATIVE SUBALGEBRA OF MATRIX ALGEBRAS

  • Song, Young-Kwon
    • 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.

FALLING SUBALGEBRAS AND IDEALS IN BH-ALGEBRAS

  • Kim, Eun-Mi;Ahn, Sun-Shin
    • The Pure and Applied Mathematics
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    • v.19 no.3
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    • pp.251-262
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    • 2012
  • Based on the theory of a falling shadow which was first formulated by Wang([14]), a theoretical approach of the ideal structure in BH-algebras is established. The notions of a falling subalgebra, a falling ideal, a falling strong ideal, a falling $n$-fold strong ideal and a falling translation ideal of a BH-algebra are introduced. Some fundamental properties are investigated. Relations among a falling subalgebra, a falling ideal and a falling strong ideal, a falling $n$-fold strong ideal are stated. A relation between a fuzzy subalgebra/ideal and a falling subalgebra/ideal is provided.

INTUITIONISTIC FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRAS

  • Hong, Sung-Min;Kim, Kyung-Ho;Jun, Young-Bae
    • Journal of applied mathematics & informatics
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    • v.8 no.1
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    • pp.261-272
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    • 2001
  • The intuitionistic fuzzification of a subalgebra in a BCK/BCI-algebra is considered, and related results are investigated. The notion of equivalence relations on the family of all intuitionistic fuzzy subalgebras of a BCK/BCI-algebra is introduced, and then some properties are discussed.

MAXIMALITY PRESERVING CONSTRUCTIONS OF MAXIMAL COMMUTATIVE SUBALGEBRAS OF MATRIX ALGEBRA

  • Song, Young-Kwon
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.2
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    • pp.295-306
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    • 2012
  • Let (R, $m_R$, k) be a local maximal commutative subalgebra of $M_n$(k) with nilpotent maximal ideal $m_R$. In this paper, we will construct a maximal commutative subalgebra $R^{ST}$ which is isomorphic to R and study some interesting properties related to $R^{ST}$. Moreover, we will introduce a method to construct an algebra in $MC_n$(k) with i($m_R$) = n and dim(R) = n.

NIL SUBSETS IN BCH-ALGEBRAS

  • Jun, Young-Bae;Roh, Eun-Hwan
    • East Asian mathematical journal
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    • v.22 no.2
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    • pp.207-213
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    • 2006
  • Using the notion of nilpotent elements, the concept of nil subsets is introduced, and related properties are investigated. We show that a nil subset on a subalgebra (resp. (closed) ideal) is a subalgebra (resp. (closed) ideal). We also prove that in a nil algebra every ideal is a subalgebra.

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A SOFT TRANSFER AND SOFT ALGEBRAIC EXTENSION OF INT-SOFT SUBALGEBRAS AND IDEALS IN BCK/BCI-ALGEBRAS

  • JUN, YOUNG BAE;LEE, KYOUNG JA
    • Communications of the Korean Mathematical Society
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    • v.30 no.4
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    • pp.339-348
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    • 2015
  • Using the notion of soft sets, the concepts of the soft transfer, support and soft algebraic extension of an int-soft subalgebra and ideal in BCK/BCI-algebras are introduced, and related properties are investigated. Conditions for a soft set to be an int-soft subalgebra and ideal are provided. Regarding the notion of support, conditions for the soft transfer of a soft set to be an int-soft subalgebra and ideal are considered.