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Surjective-Buchsbaum modules over Cohen-Macaulay local rings. (English) Zbl 0814.13017
In 1987 Goto proved that over regular local rings, there exist only finitely many isomorphism classes of indecomposable maximal Buchsbaum modules. In this paper we shall establish a structure theorem for maximal surjective Buchsbaum modules of finite injective dimension over Cohen- Macaulay local rings, that naturally improves Goto’s result. The assumption on the injective dimension is crucial; it cannot be replaced with the finiteness of projective dimension. We shall construct, over certain Cohen-Macaulay local rings, infinitely many non-isomorphic indecomposable maximal surjective Buchsbaum modules of finite projective dimension.
Reviewer: T.Kawasaki (Tokyo)

MSC:
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13D05 Homological dimension and commutative rings
13C14 Cohen-Macaulay modules
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