Projectivity and flatness over the endomorphism ring of a finitely generated comodule

T. Guédénon

Abstract: Let $k$ be a commutative ring, $A$ a $k$-algebra, $\cal C$ an $A$-coring that is projective as a left $A$-module, $^*{\cal C}$ the dual ring of ${\cal C}$ and $\Lambda$ a right $\cal C$-comodule that is finitely generated as a left $^*{\cal C}$-module. We give necessary and sufficient conditions for projectivity and flatness of a module over the endomorphism ring $End^{\cal C}(\Lambda)$. If $\cal C$ contains a grouplike element, we can replace $\Lambda$ with $A$.

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