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

T. Guédénon

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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