Geodesic
Projectivity and flatness over the graded ring of semi-coinvariants
Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 42-56.

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Let k be a field, C a bialgebra with bijective antipode, A a right C-comodule algebra, G any subgroup of the monoid of grouplike elements of C. We give necessary and sufficient conditions for the projectivity and flatness over the graded ring of semi-coinvariants of A. When A and C are commutative and G is any subgroup of the monoid of grouplike elements of the coring A⊗C, we prove similar results for the graded ring of conormalizing elements of A. 
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     author = {T. Gu\'ed\'enon},
     title = {Projectivity and flatness over the graded ring of semi-coinvariants},
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     year = {2010},
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T. Guédénon. Projectivity and flatness over the graded ring of semi-coinvariants. Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 42-56. https://geodesic-test.mathdoc.fr/item/ADM_2010_10_1_a4/