Abstract
This paper deals with the convolution operations on the set of functions between bounded lattices. Firstly, we show a subset of the set of functions that is both a bisemilattice and a Birkhoff system under the convolution operations and then show another subset of the set of functions that is a bounded distributive lattice under the convolution operations, while the domain lattice of the functions does not need to be distributive.
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Notes
A complete lattice L is called a frame (see e.g., Birkhoff 1967) if it satisfies the meet continuity property: for any \(a\in L\) and any \(\emptyset \subset B\subseteq L\), it holds that \(a\wedge (\bigvee _{b\in B} b)=\bigvee _{b\in B}(a\wedge b)\).
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Communicated by A. Di Nola.
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This work is supported by National Natural Science Foundation of China (No. 61573240).
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Liu, Zq., Wang, Xp. Two examples of subalgebras of the set of functions between bounded lattices. Soft Comput 23, 12233–12240 (2019). https://doi.org/10.1007/s00500-019-04214-w
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DOI: https://doi.org/10.1007/s00500-019-04214-w