• Title, Summary, Keyword: lattice (H) implication algebra

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LI-ideals in lattice implication algebras

  • Jun, Young-Bae;Roh, Eun-Hwan;Yang Xu
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.13-24
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    • 1998
  • We define an LI-ideal of a lattice implication algebra and show that every LI-ideal is a lattice ideal. We give an exampl that a lattice ideal may not be an LI-ideal, and show that every lattice ideal is an LI-ideal in a lattice H implication algebra. we discuss the relationship between filters and LI-ideals, and study how to generate an LI-ideal by a set. We construct the quotient structure by using an LI-ideal, and study the properties of LI-ideals related to implication homomorphisms.

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ON FUZZY IMPLICATIVE FILTERS OF LATTICE IMPLICATION ALGEBRAS

  • Zhu, Yiquan;Zhang, Qun;Roh, Eun-Hwan
    • Communications of the Korean Mathematical Society
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    • v.18 no.4
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    • pp.621-628
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    • 2003
  • We investigate some related properties of fuzzy filters and fuzzy implicative filters in lattice implication algebras. We find a characterization of fuzzy filters and fuzzy implicative filters, and we discuss a relation between fuzzy filters and fuzzy implicative filters in lattice implication algebras. Also we give an extension theorem of fuzzy implicative filters.

Remarks on the Valid Equations in Lattice Implication Algebras

  • JEONG, JOOHEE
    • Kyungpook Mathematical Journal
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    • v.43 no.4
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    • pp.539-545
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    • 2003
  • We present a set of equations that axiomatizes the class of all lattice implication algebras. The construction is different from the one given in [7], and the proof is direct: i.e., it does not rely on results from outside the realm of the lattice implication algebras, such as the theory of BCK-algebras. Then we show that the lattice H implication algebras are nothing more than the familiar Boolean algebras. Finally we obtain some negative results for the embedding of lattice implication algebras into Boolean algebras.

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ON LI-IDEALS AND PRIME LI-IDEALS OF LATTICE IMPLICATION ALGEBRAS

  • Jun, Young-Bae
    • Journal of the Korean Mathematical Society
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    • v.36 no.2
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    • pp.369-380
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    • 1999
  • As a continuation of the paper [3], in this paper we investigate the further properties on LI-ideals, and show that how to generate an LI-ideal by both and LI-ideal and an element. We define a prime LI-ideal, and give an equivalent condition for a proper LI-ideal to be prime. Using this result, we establish the extension property and prime LI-ideal theorem.

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