Projectivity and Flatness over the Colour Endomorphism Ring of a Finitely Generated Graded Comodule

Projectivity and Flatness over the Endomorphism Ring of a Finitely Generated Comodule

Let k be a commutative ring, A a k-algebra, C an A-coring that is projective as a left A-module, ∗C the dual ring of C and Λ a right C-comodule that is finitely generated as a left ∗C-module. We give necessary and sufficient conditions for projectivity and flatness of a module over the endomorphism ring EndC(Λ). If C contains a grouplike element, we can replace Λ with A.

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

Let A be a ring, and Λ a finitely generated A-module. We give necessary and sufficient conditions for projectivity and flatness of a module over the endomorphism ring of Λ.

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

Projectivity and flatness over the graded ring of normalizing elements

Let k be a field, H a cocommutative bialgebra, A a commutative left H-module algebra, Hom(H,A) the k-algebra of the k-linear maps from H to A under the convolution product, Z(H,A) the submonoid of Hom(H,A) whose elements satisfy the cocycle condition and G any subgroup of the monoid Z(H,A). We give necessary and sufficient conditions for the projectivity and flatness over the graded ring of nor...

Coinduction Functor and Simple Comodules *

Consider a coring with exact rational functor, and a finitely generated and projective right comodule. We construct a functor (coinduction functor) which is right adjoint to the hom-functor represented by this comodule. Using the coinduction functor, we establish a bijective map between the set of representative classes of torsion simple right comodules and the set of representative classes of ...