A modular characterization of supersolvable lattices
Stephan Foldes, Russ Woodroofe
TL;DR
This paper introduces a new modular relation-based characterization of supersolvable lattices, replacing the previous gradedness condition with an additional modularity condition on a chain of left-modular elements.
Contribution
It provides a novel characterization of supersolvable lattices using modularity relations, broadening the understanding of their structural properties.
Findings
Supersolvable lattices can be characterized by a modular relation.
The new characterization replaces gradedness with a modularity condition.
This approach simplifies the understanding of supersolvability in lattices.
Abstract
We characterize supersolvable lattices in terms of a certain modular type relation. McNamara and Thomas earlier characterized this class of lattices as those graded lattices having a maximal chain that consists of left-modular elements. Our characterization replaces the condition of gradedness with a second modularity condition on the maximal chain of left-modular elements.
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