The only regular inclines are distributive lattices
Song-Chol Han, Hak-Rim Ri
TL;DR
This paper proves that the only regular inclines are distributive lattices, showing that no noncommutative regular inclines exist, thus clarifying the structure of inclines in algebra.
Contribution
It establishes a complete characterization of regular inclines as distributive lattices, resolving a key question in the algebraic theory of inclines.
Findings
Regular inclines are exactly distributive lattices
No noncommutative regular inclines exist
Regular inclines have a lattice structure
Abstract
An incline is an additively idempotent semiring in which the product of two elements is always less than or equal to either factor. This paper proves that the only regular inclines are distributive lattices, which also implies that there is no noncommutative regular incline.
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Taxonomy
TopicsFuzzy and Soft Set Theory · Advanced Algebra and Logic · Rough Sets and Fuzzy Logic