Showing papers on "Global dimension published in 1980"
01 Jan 1980
TL;DR: In this paper, a commutative ring with identity is considered, and it is shown that the ring R is strongly Laskerian if each ideal of R is a finite intersection of primary ideals.
Abstract: Let R be a commutative ring with identity. An ideal Q of R is primary if each zero divisor of the ring R/ Q is nilpotent, and Q is strongly primary if Q is primary and contains a power of its radical. In the terminology of Bourbaki [B, Ch. IV, pp. 295, 298], the ring R is Laskerian if each ideal of R is a finite intersection of primary ideals, and R is strongly Laskerian if each ideal of R is a finite intersection of strongly primary ideals. It is well known that
39 citations
14 citations
TL;DR: In this article, the existence of a right artinian quotient ring Q(R) for any K-homogeneous ring R with right Krull dimension whose nil radical N is weakly right ideal invariant was proved.
14 citations
13 citations
TL;DR: In this article, the authors studied the stable rank of Gelfand rings by sheaves of modules and introduced the Cech covering dimension of their maximal spectrums, which can be compared to those for vector bundles over a finite dimensional paracompact space.
10 citations
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01 Jun 1980
6 citations
TL;DR: In this paper, it was shown that for a reduced separable analytic k-algebra A, with k being a field, a necessary condition for the finite differential module of A to have finite homological dimension is that the canonical module of a kalgebra is free.
Abstract: It will be shown that for a reduced separable analytic k-algebra A, with k being a field, a necessary condition for the finite differential module of A to have finite homological dimension is that the canonical module of A is free. This generalizes a result of T. Matsuoka and Y. Aoyama concerning almost complete intersections. In case that A is a normal domain and smooth in codimension ≤1 an analogous statement can be made for the module of derivations and the module of Zariski differentials of A.
5 citations
TL;DR: In this paper, a passage from the category of modules to the derived category gives insight into some classical results of homological dimension theory, and also yields a proof of the nondegeneracy of the Yoneda multiplication, where the argument is a noetherian module (or a finite complex with noetherians) and is a regular local ring.
Abstract: Passage from the category of modules to the derived category gives insight into some classical results of homological dimension theory, and also yields a proof of the nondegeneracy of the Yoneda multiplication, where the argument is a noetherian module (or a finite complex with noetherian homology) and is a regular local ring. Bibliography: 9 titles.