Representable equivalences for closed categories of modules

Sonia Dal Pio; Adalberto Orsatti

Displaying similar documents to “Representable equivalences for closed categories of modules”

Representable equivalences between categories of modules and applications

Claudia Menini, Adalberto Orsatti (1989)

Rendiconti del Seminario Matematico della Università di Padova

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Properties of G-atoms and full Galois covering reduction to stabilizers

Piotr Dowbor (2000)

Colloquium Mathematicae

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Given a group G of k-linear automorphisms of a locally bounded k-category R it is proved that the endomorphism algebra $E n d_{R} (B)$ of a G-atom B is a local semiprimary ring (Theorem 2.9); consequently, the injective $E n d_{R} (B)$ -module ${(E n d_{R} (B))}^{*}$ is indecomposable (Corollary 3.1) and the socle of the tensor product functor $- \otimes_{R} B^{*}$ is simple (Theorem 4.4). The problem when the Galois covering reduction to stabilizers with respect to a set U of periodic G-atoms (defined by the functors $Φ^{U} : ∐_{B \in U} m o d k G_{B} \to m o d (R / G)$ and $Ψ^{U} : m o d (R / G) \to \prod_{B \in U} m o d k G_{B}$ )is full (resp. strictly full)...

A Morita type theorem for a sort of quotient categories

Simion Breaz (2005)

Czechoslovak Mathematical Journal

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We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories.