Proceedings of the American Mathematical Society, 1996
Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted b... more Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by δ n R (M) for each module M and for each integer n. We propose a conjecture asking if δ n R (R/m) = 0 for any positive integers n and. We prove that this is true provided the associated graded ring of R has depth not less than dim R − 1. Furthermore we show that there are only finitely many possibilities for a pair of positive integers (n,) for which δ n R (R/m) > 0.
Cohen-Macaulay dimension for modules over a commutative ring has been defined by A. A. Gerko. Tha... more Cohen-Macaulay dimension for modules over a commutative ring has been defined by A. A. Gerko. That is a homological invariant sharing many properties with projective dimension and Gorenstein dimension. The main purpose of this paper is to extend the notion of Cohen-Macaulay dimension for modules over commutative noetherian local rings to that for bounded complexes over non-commutative noetherian rings.
We propose to define the notion of abstract local cohomology functors. The ordinary local cohomol... more We propose to define the notion of abstract local cohomology functors. The ordinary local cohomology functor RΓ I with support in the closed subset defined by an ideal I and the generalized local cohomology functor RΓ I,J defined in [16] are characterized as elements of the set of all the abstract local cohomology functors.
We develop the theory of Gröbner bases for ideals in a polynomial ring with countably infinite va... more We develop the theory of Gröbner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-one correspondences among various sets of partitions by using division algorithm.
Proceedings of the American Mathematical Society, 1996
Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted b... more Let (R, m) be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by δ n R (M) for each module M and for each integer n. We propose a conjecture asking if δ n R (R/m) = 0 for any positive integers n and. We prove that this is true provided the associated graded ring of R has depth not less than dim R − 1. Furthermore we show that there are only finitely many possibilities for a pair of positive integers (n,) for which δ n R (R/m) > 0.
Cohen-Macaulay dimension for modules over a commutative ring has been defined by A. A. Gerko. Tha... more Cohen-Macaulay dimension for modules over a commutative ring has been defined by A. A. Gerko. That is a homological invariant sharing many properties with projective dimension and Gorenstein dimension. The main purpose of this paper is to extend the notion of Cohen-Macaulay dimension for modules over commutative noetherian local rings to that for bounded complexes over non-commutative noetherian rings.
We propose to define the notion of abstract local cohomology functors. The ordinary local cohomol... more We propose to define the notion of abstract local cohomology functors. The ordinary local cohomology functor RΓ I with support in the closed subset defined by an ideal I and the generalized local cohomology functor RΓ I,J defined in [16] are characterized as elements of the set of all the abstract local cohomology functors.
We develop the theory of Gröbner bases for ideals in a polynomial ring with countably infinite va... more We develop the theory of Gröbner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-one correspondences among various sets of partitions by using division algorithm.
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Papers by Yuji Yoshino