Flat model structures under excellent extensions

Abstract

We prove that the weak equivalences, cofibrations and fibrations in Gillespie’s flat model structure are invariant under excellent extensions of rings. As applications, the flat and cotorsion dimensions of unbounded complexes along excellent extensions are investigated, and moreover, some homological invariant properties under excellent extensions are studied in the present framework of complexes.

Mathematics Subject Classification (2010): 16S35, 18G20, 18G35.

Keywords: Flat model structure, excellent extension, flat dimension, cotorsion dimension