Homological invariant properties under cleft extensions

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 θ-extensions and Morita context rings are given.

19 pages