Projectivity and flatness over the colour endomorphism ring of a finitely generated graded comodule. (English) Zbl 1192.16001
The paper under review gives some conditions to test projectivity or flatness of modules over the color endomorphism ring of a finitely generated graded \(\mathcal C\)-comodule, where \(\mathcal C\) is a graded coring. To test projectivity the author proposes two criteria and also formulates one sufficient and one necessary condition. To test flatness the author proposes four criteria of slightly different nature.
Reviewer: Volodymyr Mazorchuk (Uppsala)
MSC:
16D40 | Free, projective, and flat modules and ideals in associative algebras |
16T15 | Coalgebras and comodules; corings |
16S50 | Endomorphism rings; matrix rings |
16W50 | Graded rings and modules (associative rings and algebras) |