2,375 research outputs found
Model Structures on Exact Categories
We define model structures on exact categories which we call exact model
structures. We look at the relationship between these model structures and
cotorsion pairs on the exact category. In particular, when the underlying
category is weakly idempotent complete we get Hovey's one-to-one correspondence
between model structures and complete cotorsion pairs. We classify the right
and left homotopy relation in terms of the cotorsion pairs and look at examples
of exact model structures. In particular, we see that given any hereditary
abelian model category, the full subcategories of cofibrant, fibrant and
cofibrant-fibrant subobjects each have natural exact model structures
equivalent to the original model structure. These model structures each have
interesting characteristics. For example, the cofibrant-fibrant subobjects form
a Frobenius category whose stable category is the same thing as the homotopy
category of its model structure.Comment: 17 page
Model structures on modules over Ding-Chen rings
An -FC ring is a left and right coherent ring whose left and right self
FP-injective dimension is . The work of Ding and Chen in \cite{ding and chen
93} and \cite{ding and chen 96} shows that these rings possess properties which
generalize those of -Gorenstein rings. In this paper we call a (left and
right) coherent ring with finite (left and right) self FP-injective dimension a
Ding-Chen ring. In case the ring is Noetherian these are exactly the Gorenstein
rings. We look at classes of modules we call Ding projective, Ding injective
and Ding flat which are meant as analogs to Enochs' Gorenstein projective,
Gorenstein injective and Gorenstein flat modules. We develop basic properties
of these modules. We then show that each of the standard model structures on
Mod-, when is a Gorenstein ring, generalizes to the Ding-Chen case. We
show that when is a commutative Ding-Chen ring and is a finite group,
the group ring is a Ding-Chen ring.Comment: 12 page
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