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Research on the Characteristic of the Five-Element Sub-lattice

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International Conference on Oriental Thinking and Fuzzy Logic

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 443))

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Abstract

We have already known in the sense of isomorphism, there are five five-element lattices. In this paper, we establish some important results about the characteristic of a lattice that contains these five five-element lattices.

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References

  1. Baker, K.: Equational axioms for classes of lattices. Bull. Am. Math. Soc. 77, 97–102 (1971)

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  2. Birkhoff, G.: Lattice Theory, vol. 25, 3rd edn. American Mathematical Society Colloquium Publications, Providence (1967). MR 37 2638

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  3. Freese, R.: Varieties generated by modular lattices of width four. Ph.D. Thesis, California Institute of Technology (1972)

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  4. Gratzer, G.: General Lattice Theory. Academic Press, New York (2003)

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Acknowledgments

This research was financially supported by the National Natural Science Foundation of China (No. 11271040 and 10871017).

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Correspondence to Hai-feng Zhang .

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© 2016 Springer International Publishing Switzerland

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Zhang, Hf., Zhou, M., Zhang, Gj. (2016). Research on the Characteristic of the Five-Element Sub-lattice. In: Cao, BY., Wang, PZ., Liu, ZL., Zhong, YB. (eds) International Conference on Oriental Thinking and Fuzzy Logic. Advances in Intelligent Systems and Computing, vol 443. Springer, Cham. https://doi.org/10.1007/978-3-319-30874-6_58

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  • DOI: https://doi.org/10.1007/978-3-319-30874-6_58

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30873-9

  • Online ISBN: 978-3-319-30874-6

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