The category of groupoid graded modules

• Autorzy: Patrik Lundström
• Języki publikacji: EN

Abstrakty

EN

We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely presented, projective, injective, essential, small, and flat. We also investigate when exact sequences are pure in R-gr. Some relevant counterexamples are indicated.

Kategorie tematyczne

• 16D10: General module theory
• 16D50: Injective modules, self-injective rings
• 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality
• 16D40: Free, projective, and flat modules and ideals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 100
• Numer: 2
• Strony: 195-211

Daty

wydano

2004

Twórcy

autor

Patrik Lundström

• Department of Informatics and Mathematics, University of Trollhättan/Uddevalla, Gärdhemsvägen 4, Box 957, 461 29 Trollhättan, Sweden

Identyfikatory

DOI

10.4064/cm100-2-4