Flat Comodules and Perfect Coalgebras

Autor:	Daniel Simson, Juan Cuadra
Rok vydání:	2007
Předmět:	Combinatorics Algebra and Number Theory Mathematics::K-Theory and Homology Grothendieck category Computer Science::Logic in Computer Science Mathematics::Quantum Algebra Mathematics::Category Theory Coalgebra Mathematics::Rings and Algebras Field (mathematics) Injective function Mathematics
Zdroj:	Communications in Algebra. 35:3164-3194
ISSN:	1532-4125 0092-7872
DOI:	10.1080/00914030701409908
Popis:	Stenstrom introduced the notion of flat object in a locally finitely presented Grothendieck category 𝒜. In this article we investigate this notion in the particular case of the category 𝒜 = C-Comod of left C-comodules, where C is a coalgebra over a field K. Several characterizations of flat left C-comodules are given and coalgebras having enough flat left C-comodules are studied. It is shown how far these coalgebras are from being left semiperfect. As a consequence, we give new characterizations of a left semiperfect coalgebra in terms of flat comodules. Left perfect coalgebras are introduced and characterized in analogy with Bass's Theorem P. Coalgebras whose injective left C-comodules are flat are discussed and related to quasi-coFrobenius coalgebras.
Databáze:	OpenAIRE
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