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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 68))

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Abstract

In this short paper we define a filter of a commutative residuated lattice and prove that, for any commutative residuated lattice L, the lattice Fil(L) of all filters of L is isomorphic to the congruence lattice Con(L) of L, that is,

$$Fil(L) \cong Con(L)$$

.

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Kondo, M. (2010). Filters on Commutative Residuated Lattices. In: Huynh, VN., Nakamori, Y., Lawry, J., Inuiguchi, M. (eds) Integrated Uncertainty Management and Applications. Advances in Intelligent and Soft Computing, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11960-6_32

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  • DOI: https://doi.org/10.1007/978-3-642-11960-6_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11959-0

  • Online ISBN: 978-3-642-11960-6

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