Multiplicative structure of generalized Koszul complexes

Author:
Eugene H. Gover

Journal:
Trans. Amer. Math. Soc. **185** (1973), 287-307

MSC:
Primary 13D99

DOI:
https://doi.org/10.1090/S0002-9947-1973-0332769-7

MathSciNet review:
0332769

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Abstract: A multiplicative structure is defined for the generalized Koszul complexes associated with the exterior powers of a map where *R* is a commutative ring and . With this structure becomes a differential graded *R*-algebra over which each , is a DG right -module. For and , the multiplication and all higher order Massey operations of are shown to be trivial. When *R* is noetherian local, is used to define a class of local rings which includes the local complete intersections. The rings obtained for are Cohen-Macaulay but not Gorenstein. Their Betti numbers and Poincaré series are computed but these do not characterize the rings.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0332769-7

Keywords:
Generalized Koszul complex,
differential graded algebra,
trivial multiplicative structure,
Massey operations,
generalized local complete intersection,
Betti numbers,
Poincaré series

Article copyright:
© Copyright 1973
American Mathematical Society