Dimension and decomposition in modular upper-continuous lattices
Jos\'e R\'ios Montes, Angel Zald\'ivar
TL;DR
This paper extends the concepts of decomposition and dimension theories from module categories to the setting of complete modular upper-continuous lattices, providing a new perspective on lattice structures.
Contribution
It introduces a translation of dimension theory from module categories to the lattice environment, bridging two mathematical frameworks.
Findings
Dimension theory is successfully adapted to complete modular upper-continuous lattices.
The translation preserves key properties of the original module category theories.
New insights into lattice decomposition and dimension emerge from this translation.
Abstract
We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.
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