On free elementary ZpCp lattices
Gabriele Nebe
TL;DR
This paper characterizes free elementary lattices over the group ring of cyclic groups of prime order, showing they decompose orthogonally into simpler components, aiding understanding of their structure.
Contribution
It proves that all such free elementary lattices can be orthogonally decomposed into free unimodular and p-modular lattices, providing a structural classification.
Findings
All elementary free $ ext{Z}_p C_p$-lattices admit orthogonal decomposition.
Decomposition into free unimodular and p-modular lattices.
Enhanced understanding of lattice structure over group rings.
Abstract
We show that all elementary lattices that are free -modules admit an orthogonal decomposition into a sum of free unimodular and -modular lattices.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Rings, Modules, and Algebras