• Title, Summary, Keyword: $\mathcal{N}$-ideals

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COUPLED N-STRUCTURES APPLIED TO IDEALS IN d-ALGEBRAS

  • Ahn, Sun Shin;Ko, Jung Mi
    • Communications of the Korean Mathematical Society
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    • v.28 no.4
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    • pp.709-721
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    • 2013
  • The notions of coupled N-subalgebra, coupled (positive implicative) N-ideals of $d$-algebras are introduced, and related properties are investigated. Characterizations of a coupled $\mathcal{N}$-subalgebra and a coupled (positive implicative) $\mathcal{N}$-ideals of $d$-algebras are given. Relations among a coupled $\mathcal{N}$-subalgebra, a coupled $\mathcal{N}$-ideal and a coupled positive implicative $\mathcal{N}$-ideal of $d$-algebras are discussed.

IDEAL THEORY OF d-ALGEBRAS BASED ON $\mathcal{N}$-STRUCTURES

  • Ahn, Sun-Shin;Han, Gyeong-Ho
    • Journal of applied mathematics & informatics
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    • v.29 no.5_6
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    • pp.1489-1500
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    • 2011
  • The notions of $\mathcal{N}$-subalgebra, (positive implicative) $\mathcal{N}$-ideals of d-algebras are introduced, and related properties are investigated. Characterizations of an $\mathcal{N}$-subalgebra and a (positive implicative) $\mathcal{N}$-ideals of d-algebras are given. Relations between an $\mathcal{N}$-subalgebra, an $\mathcal{N}$-ideal and a positive implicative N-ideal of d-algebras are discussed.

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 COUPLED 𝒩-STRUCTURE WITH AN APPLICATION IN A SUBTRACTION ALGEBRA

  • Williams, D.R. Prince;Ahn, Sun Shin;Jun, Young Bae
    • Honam Mathematical Journal
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    • v.36 no.4
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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.

APPLICATIONS OF COUPLED N-STRUCTURES IN BH-ALGEBRAS

  • Seo, Min Jeong;Ahn, Sun Shin
    • Honam Mathematical Journal
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    • v.34 no.4
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    • pp.585-596
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    • 2012
  • The notions of a $\mathcal{N}$-subalgebra, a (strong) $\mathcal{N}$-ideal of BH-algebras are introduced, and related properties are investigated. Characterizations of a coupled $\mathcal{N}$-subalgebra and a coupled (strong) $\mathcal{N}$-ideals of BH-algebras are given. Relations among a coupled $\mathcal{N}$-subalgebra, a coupled $\mathcal{N}$-ideal and a coupled strong $\mathcal{N}$ of BH-algebras are discussed.

SOME REMARKS ON CATEGORIES OF MODULES MODULO MORPHISMS WITH ESSENTIAL KERNEL OR SUPERFLUOUS IMAGE

  • Alahmadi, Adel;Facchini, Alberto
    • Journal of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.557-578
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    • 2013
  • For an ideal $\mathcal{I}$ of a preadditive category $\mathcal{A}$, we study when the canonical functor $\mathcal{C}:\mathcal{A}{\rightarrow}\mathcal{A}/\mathcal{I}$ is local. We prove that there exists a largest full subcategory $\mathcal{C}$ of $\mathcal{A}$, for which the canonical functor $\mathcal{C}:\mathcal{C}{\rightarrow}\mathcal{C}/\mathcal{I}$ is local. Under this condition, the functor $\mathcal{C}$, turns out to be a weak equivalence between $\mathcal{C}$, and $\mathcal{C}/\mathcal{I}$. If $\mathcal{A}$ is additive (with splitting idempotents), then $\mathcal{C}$ is additive (with splitting idempotents). The category $\mathcal{C}$ is ample in several cases, such as the case when $\mathcal{A}$=Mod-R and $\mathcal{I}$ is the ideal ${\Delta}$ of all morphisms with essential kernel. In this case, the category $\mathcal{C}$ contains, for instance, the full subcategory $\mathcal{F}$ of Mod-R whose objects are all the continuous modules. The advantage in passing from the category $\mathcal{F}$ to the category $\mathcal{F}/\mathcal{I}$ lies in the fact that, although the two categories $\mathcal{F}$ and $\mathcal{F}/\mathcal{I}$ are weakly equivalent, every endomorphism has a kernel and a cokernel in $\mathcal{F}/{\Delta}$, which is not true in $\mathcal{F}$. In the final section, we extend our theory from the case of one ideal$\mathcal{I}$ to the case of $n$ ideals $\mathcal{I}_$, ${\ldots}$, $\mathca{l}_n$.