Homological invariant properties under cleft extensions
Li Liang, Yajun Ma, Gang Yang
TL;DR
This paper investigates how the Gorenstein weak global dimension behaves under cleft extensions of rings, showing invariance under certain conditions and exploring related singularity categories and applications.
Contribution
It introduces new results on the invariance of Gorenstein weak global dimension under cleft extensions and compares related singularity categories.
Findings
Finiteness of Gorenstein weak global dimension is invariant under certain cleft extensions.
Comparison of relative singularity categories with respect to flat-cotorsion modules.
Applications to { heta}-extensions and Morita context rings.
Abstract
We study the behavior of the Gorenstein weak global dimension under a cleft extension of rings; we prove that under some mild conditons the finiteness of the Gorenstein weak global dimension is invariant. Moreover, we compare the relative singularity categories with respect to flat-cotorsion modules under a cleft extension of rings. Some applications to {\theta}-extensions and Morita context rings are given.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory