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

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.

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

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, C a graded A-coring that is projective as a right A-module, C∗ the graded dual ring of C and Λ a left graded C-comodule that is finitely generated as a graded right C∗-module. We give necessary and sufficient conditions for projectivity and flatness of a graded modul...

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.

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...