Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 49, No. 2, pp. 399-408 (2008)

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

T. Guédénon

1120 avenue Fournier, Québec, QC, G1V 2H8, Canada,

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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Electronic version published on: 18 Sep 2008. This page was last modified: 28 Jan 2013.

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