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Involutive Residuated Lattices Based on Modular and Distributive Lattices

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Abstract

An involutive residuated lattice (IRL) is a lattice-ordered monoid possessing residual operations and a dualizing element. We show that a large class of self-dual lattices may be endowed with an IRL structure, and give examples of lattices which fail to admit IRLs with natural algebraic conditions. A classification of all IRLs based on the modular lattices M n is provided.

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Correspondence to Jeffrey S. Olson.

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Olson, J.S. Involutive Residuated Lattices Based on Modular and Distributive Lattices. Order 31, 373–389 (2014). https://doi.org/10.1007/s11083-013-9307-3

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  • DOI: https://doi.org/10.1007/s11083-013-9307-3

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