منابع مشابه
Bounding Projective Dimension
The use of algorithms in algebra as well as the study of their complexity was initiated before the advent of modern computers. Hermann [25] studied the ideal membership problem, i.e determining whether a given polynomial is in a fixed homogeneous ideal, and found a doubly exponential bound on its computational complexity. Later Mayr and Meyer [31] found examples which show that her bound was ne...
متن کاملFinitistic Dimension through Infinite Projective Dimension
We show that an artin algebra Λ having at most three radical layers of infinite projective dimension has finite finitistic dimension, generalizing the known result for algebras with vanishing radical cube. We also give an equivalence between the finiteness of fin.dim.Λ and the finiteness of a given class of Λ-modules of infinite projective dimension.
متن کاملFinite Flat and Projective Dimension
known as the left big finitistic projective dimension of A, is finite. Here pdM denotes the projective dimension of M . Unfortunately, this number is not known to be finite even if A is a finite dimensional algebra over a field, where, indeed, its finiteness is a celebrated conjecture. On the other hand, for such an algebra, finite flat certainly implies finite projective dimension, simply beca...
متن کاملThe Koszul Complex in Projective Dimension One
Let R be a noetherian ring and M a finite R-module. With a linear form χ on M one associates the Koszul complex K(χ). If M is a free module, then the homology of K(χ) is well-understood, and in particular it is grade sensitive with respect to Imχ. In this note we investigate the case of a module M of projective dimension 1 (more precisely, M has a free resolution of length 1) for which the firs...
متن کاملThe Koszul Complex in Projective Dimension One
Let R be a noetherian ring andM a finite R-module. With a linear form χ onM one associates the Koszul complex K(χ). IfM is a free module, then the homology of K(χ) is well-understood, and in particular it is grade sensitive with respect to Imχ. In this note we investigate the case of a module M of projective dimension 1 (more precisely, M has a free resolution of length 1) for which the first n...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2000
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(99)00067-5