• Title, Summary, Keyword: subtraction algebra

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Fuzzy ideals of subtraction algebras

  • Kim, Young-Hee;Oh, Kyong-Ah;Roh, Eun-Hawan
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.7 no.2
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    • pp.115-119
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    • 2007
  • The notion of ideals in subtraction algebras and characterizations of ideals introduced by Y.B.Jun et al. [?]. Using this idea, we consider the fuzzification of an ideal of a subtraction algebra. In this paper, we define the concept of a fuzzy ideal of a subtraction algebra and study characterizations of a fuzzy ideal. We give some conditions to show that a fuzzy set in a subtraction algebra is a fuzzy ideal of a subtraction algebra. We investigate the generalization of some properties of a fuzzy ideal of a subtraction algebra.

NEUTROSOPHIC IDEALS IN SUBTRACTION ALGEBRAS

  • Kim, Young Hie;Ahn, Sun Shin
    • Honam Mathematical Journal
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    • v.41 no.2
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    • pp.435-447
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    • 2019
  • The notions of a neutrosophic subalgebra and a neutrosohic ideal of a subtraction algebra are introduced. Characterizations of a neutrosophic subalgebra and a neutrosophic ideal are investigated. We show that the homomorphic preimage of a neutrosophic subalgebra of a subtraction algebra is a neutrosophic subalgebra, and the onto homomorphic image of a neutrosophic subalgebra of a subtraction algebra is a neutrosophic subalgebra.

SUBTRACTION ALGEBRAS WITH ADDITIONAL CONDITIONS

  • Jun, Young-Bae;Kim, Young-Hee;Oh, Kyong-Ah
    • Communications of the Korean Mathematical Society
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    • v.22 no.1
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    • pp.1-7
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    • 2007
  • Subtraction algebras with additional conditions, so called complicated subtraction algebras, are introduced, and several properties are investigated. In a complicated subtraction algebra, characterizations of ideals are provided, and showed that the set of all ideals in a complicated subtraction algebra is a complete lattice.

ORDER SYSTEMS, IDEALS AND RIGHT FIXED MAPS OF SUBTRACTION ALGEBRAS

  • Jun, Young-Bae;Park, Chul-Hwan;Roh, Eun-Hwan
    • Communications of the Korean Mathematical Society
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    • v.23 no.1
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    • pp.1-10
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    • 2008
  • Conditions for an ideal to be irreducible are provided. The notion of an order system in a subtraction algebra is introduced, and related properties are investigated. Relations between ideals and order systems are given. The concept of a fixed map in a subtraction algebra is discussed, and related properties are investigated.

On Near Subtraction Semigroups (Near Subtraction Semigroups에 관한 연구)

  • Yon Yong-Ho;Kim Mi-Suk;Kim Mi-Hye
    • Proceedings of the Korea Contents Association Conference
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    • pp.406-410
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    • 2003
  • B. M. Schein([1]) considered systems of the form (${\Phi}$; ${\circ}$,-), where ${\Phi}$ is a set of functions closed under the composition "${\circ}$" of functions and the set theoretic subtraction "-". In this structure, (${\Phi}$; ${\circ}$) is a function semigroup and (${\Phi}$;-) is a subtraction algebra in the sense of [1]. He proved that every subtraction semigroup is isomorphic to a difference semigroup of invertible functions. Also this structure is closely related to the mathematical logic, Boolean algebra, Bck-algera, etc. In this paper, we define the near subtraction semigroup as a generalization of the subtraction semigroup, and define the notions of strong for it, and then we will search the general properties of this structure, the properties of ideals, and the application of it.

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N-IDEALS OF SUBTRACTION ALGEBRAS

  • Jun, Young-Bae;Kavikumar, Jacob;So, Keum-Sook
    • Communications of the Korean Mathematical Society
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    • v.25 no.2
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    • pp.173-184
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    • 2010
  • Using $\cal{N}$-structures, the notion of an $\cal{N}$-ideal in a subtraction algebra is introduced. Characterizations of an $\cal{N}$-ideal are discussed. Conditions for an $\cal{N}$-structure to be an $\cal{N}$-ideal are provided. The description of a created $\cal{N}$-ideal is established.