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Keywords:
lattice implication algebra; (ultra) $LI$-ideal; finite additive property
lattice implication algebra; (ultra) $LI$-ideal; finite additive property
Summary:
We define an ultra $LI$-ideal of a lattice implication algebra and give equivalent conditions for an $LI$-ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra $LI$-ideal.
References:
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[3] Y. B. Jun, Y. Xu and K. Y. Qin: Positive implicative and associative filters of lattice implication algebras. Bull. Korean Math. Soc. 35(1) (1998), 53–61. MR 1608994
[4] Y. Xu: Homomorphisms in lattice implication algebras. Proc. of 5th Many-Valued Logical Congress of China (1992), 206–211.
[5] Y. Xu: Lattice implication algebras. J. Southwest Jiaotong University 1 (1993), 20–27. Zbl 0966.03524
[6] Y. Xu and K. Y. Qin: On filters of lattice implication algebras. J. Fuzzy Math. 1 (1993), 251–260. MR 1230317
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