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• W2572560211 abstract "This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be embedded into the lattice $L$ such that all infima, suprema, the top and bottom elements are preserved under the embedding by defining a monotonic operator on a poset. This paper finally shows that the quotient of the set of the monotonic operators under an equivalence relation can be naturally ordered and it is a lattice if $L$ is a finite distributive lattice." @default.
• W2572560211 created "2017-01-26" @default.
• W2572560211 creator A5019827695 @default.
• W2572560211 creator A5040971537 @default.
• W2572560211 date "2017-01-14" @default.
• W2572560211 modified "2023-09-27" @default.
• W2572560211 title "Structures of lattices which can be represented as the collection of all up-sets" @default.
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• W2572560211 hasPublicationYear "2017" @default.
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