Showing papers on "Global dimension published in 1986"
TL;DR: In this article, the dimension of S(M), the symmetric algebra of M, and the components of M are identified, as well as the dimension is given by the for-mula, dim s(M) = max {dim R/p+p(M)), where R is a commutative Noetherian ring and A4 a finitely generated R-module.
60 citations
35 citations
01 Jan 1986
35 citations
TL;DR: A survey of the subject of approximate invertibility on three-dimensional manifolds can be found in this paper, where a theorem on the resolvent of a compactum is given and an essential map of spheres with an everywhere dense set of points of univalence.
Abstract: CONTENTS ??1 Survey of the subject ??2 Approximate invertibility and a theorem on three-dimensional manifolds ??3 The example of Taylor and its consequences ??4 The theorem of Edwards on the resolvent of a compactum ??5 Widths and homological dimension ??6 Essential maps of spheres with an everywhere dense set of points of univalence ??7 Homological dimension modulo pReferences
18 citations
TL;DR: In this paper, the concepts of primitive ideal and semicocritical modules with respect to a torsion theory are studied and related to the structure of torsionsfree injective modules.
Abstract: The concepts of primitive ideal and semicocritical module with respect to a torsion theory are studied and related to the structure of torsionfree injective modules. Applications are made to the study of (1) composition series with respect to a torsion theory and (2) the structure of endomorphism rings of torsionfree modules. These results are natural generalizations of the properties of certain modules over (noetherian) rings with Krull dimension.
16 citations
01 Jan 1986
13 citations
13 citations
TL;DR: In this paper, the full subcategories of R-modules L such that Exti(E,L)=0 for all injective Rmodules E for 1 ⋚i⋚n and O √i √n by Cn, and C′n respectively.
Abstract: Let R be a noetherian ring, and denote the full subcategories of R-modules L such that Exti(E,L)=0 for all injective R-modules E for 1⋚i⋚n and O⋚i⋚n by Cn, and C′n respectively. Then LeCn, if and only if every injective resolution of L is an injective resolvent of the nth cosyzygy. In this case, L is not injective if and only if its injective dimension is greater than n. If LeC′n and idN⋚n. then Hom(N,L)=0 for all R-modules N. As an application, let Kn be the nth syzygy of an injective resolvent of the nth cosyzygy of an R-module N, then there exists a homomorphism φ:N → K such that ((φ,iN), Kn • E(N)) and (φ,Kn) are preenvelopes of N for Cs and C′s respectively, for s≥n. If the global dimension of R is at most 2, then C′1 is reflective in the category of R-modules.
8 citations
TL;DR: In this article, the homological dimension and the primary decomposition of a nonperfect radical 3-generated ideal of n×n minors of a noetherian ring R involving the columns of a submatrix of M consisting of the first r columns (r ⩽ n−1).
8 citations
TL;DR: In this paper, the authors extend the results of tilted artinian algebras to orders and give complete proofs, some of which are taken directly from the artinian case.
Abstract: The aim of this note is to extend the results of tilted artinian algebras [2, 4, 3, 1] to orders. Some of the proofs carry over almost unchanged from the artinian case to the case of orders: others need considerable alteration—in particular the results on global dimensions. For the convenience of the reader we shall give complete proofs here—some are taken directly from [2]. I would like to thank C.M. Ringel who has patiently explained to me the situation for artinian algebras.
TL;DR: In this paper, the Euler characteristic of kT modules is defined as follows: if k is skew field and f a virtually polycyclic group, i.e., r contains a poly-cyclic subgroup of finite index, then every finitely generated kr' module has a finite free resolution.