TL;DR
This paper introduces the concept of a unique largest distributive quotient for any lattice, which encompasses all other distributive quotients as its quotients, providing a canonical maximal distributive structure.
Contribution
It establishes the existence and uniqueness of the largest distributive quotient for any lattice, a novel structural insight in lattice theory.
Findings
Every lattice has a unique largest distributive quotient.
All other distributive quotients are quotients of this largest one.
This quotient serves as a canonical maximal distributive structure.
Abstract
We note that each lattice has a unique largest distributive quotient, of which every distributive quotient of is itself a quotient.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras · Advanced Topology and Set Theory