3 research outputs found
Equivalences of comodule categories for coalgebras over rings
In this article we defined and studied quasi-finite comodules, the cohom
functors for coalgebras over rings. linear functors between categories of
comodules are also investigated and it is proved that good enough linear
functors are nothing but a cotensor functor. Our main result of this work
characterizes equivalences between comodule categories generalizing the
Morita-Takeuchi theory to coalgebras over rings. Morita-Takeuchi contexts in
our setting is defined and investigated, a correspondence between strict
Morita-Takeuchi contexts and equivalences of comodule categories over the
involved coalgebras is obtained. Finally we proved that for coalgebras over
QF-rings Takeuchi's representation of the cohom-functor is also valid.Comment: 30 pages, xy-pic. To appear in Jornal of pure and applied algebr
τ-complemented and τ-supplemented modules
Proper classes of monomorphisms and short exact sequences were introduced by Buchsbaum to study relative homological algebra. It was observed in abelian group theory that complement submodules induce a proper class of monomorphism and this observations were extended to modules by Stenstr\"om, Generalov, and others. In this note we consider complements and supplements with respect to (idempotent) radicals and study the related proper classes of short exact sequences.Proper classes of monomorphisms and short exact sequences were introduced by Buchsbaum to study relative homological algebra. It was observed in abelian group theory that complement submodules induce a proper class of monomorphism and this observations were extended to modules by Stenstr\"om, Generalov, and others. In this note we consider complements and supplements with respect to (idempotent) radicals and study the related proper classes of short exact sequences