Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 1, pp. 209-227 (2010)

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

T. Guédénon

110 Penworth Drive S.E., Calgary, AB, T2A 5H4, Canada, e-mail:

Abstract: Let $k$ be a field, $G$ an abelian group with a bicharacter, $A$ a colour algebra; i.e., an associative graded $k$-algebra with identity, $\mathcal{C}$ a graded $A$-coring that is projective as a right $A$-module, ${\mathcal{C}}^*$ the graded dual ring of ${\mathcal{C}}$ and $\Lambda$ a left graded $\mathcal{C}$-comodule that is finitely generated as a graded right ${\mathcal C}^*$-module. We give necessary and sufficient conditions for projectivity and flatness of a graded module over the colour endomorphism ring $^{\mathcal{C}}END(\Lambda)$.

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Electronic version published on: 27 Jan 2010. This page was last modified: 28 Jan 2013.

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