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

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

MULTIPLICATION MODULES THAT ARE FINITELY GENERATED

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...

On finitely generated modules whose first nonzero Fitting ideals are regular

A finitely generated $R$-module is said to be a module of type ($F_r$) if its $(r-1)$-th Fitting ideal is the zero ideal and its $r$-th Fitting ideal is a regular ideal. Let $R$ be a commutative ring and $N$ be a submodule of  $R^n$ which is generated by columns of  a matrix $A=(a_{ij})$ with $a_{ij}in R$ for all $1leq ileq n$, $jin Lambda$, where $Lambda $ is a (possibly infinite) index set.  ...