Classification of certain cellular classes of chain complexes
Jonas Kiessling
TL;DR
This paper provides a complete classification of the cellular lattice structure of perfect chain complexes over a local commutative ring with a principal maximal ideal satisfying m^2=0.
Contribution
It offers a comprehensive description of the cellular lattice for perfect chain complexes in a specific algebraic setting, filling a gap in the understanding of such structures.
Findings
Complete description of the cellular lattice achieved
Characterization of perfect chain complexes over the ring
Insights into algebraic structure of chain complexes
Abstract
Let (R, m) be a local commutative ring. Suppose that m is principal and that m^2 = 0. We give a complete description of the cellular lattice of perfect chain complexes of modules over this ring.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Rings, Modules, and Algebras · Homotopy and Cohomology in Algebraic Topology