منابع مشابه
On the Goldie Dimension of Hereditary Rings and Modules
We find a bound for the Goldie dimension of hereditary modules in terms of the cardinality of the generator sets of its quasi-injective hull. Several consequences are deduced. In particular, it is shown that every right hereditary module with countably generated quasi-injective hull is noetherian. Or that every right hereditary ring with finitely generated injective hull is artinian, thus answe...
متن کاملOn the Splitting of the Dual Goldie Torsion Theory
The splitting of the Goldie (or singular) torsion theory has been extensively studied. Here we determine an appropriate dual Goldie torsion theory, discuss its splitting and answer in the negative a question proposed by Özcan and Harmancı as to whether the splitting of the dual Goldie torsion theory implies the ring to be quasi-Frobenius.
متن کاملNote on Metric Dimension
The metric dimension of a compact metric space is defined here as the order of growth of the exponential metric entropy of the space. The metric dimension depends on the metric, but is always bounded below by the topological dimension. Moreover, there is always an equivalent metric in which the metric and topological dimensions agree. This result may be used to define the topological dimension ...
متن کاملA note on sufficient dimension reduction
In this paper, we presented a theoretical result and then discussed possible applications of our result to SDR problems. In addition to providing insights into existing SDR methods when Y is univariate; our theorem also applies to multivariate responses, especially when the response takes the form of ðY ;W Þ, where Y is a continuous variable and W is categorical. r 2007 Elsevier B.V. All rights...
متن کاملA Note on Simplicial Dimension Shifting
We discuss a simplicial dimension shift which associates to each n-manifold an n−1-manifold. As a corollary we show that an invariant which was recently proposed by Ooguri and by Crane and Yetter for the construction of 4-dimensional quantum field theories out of 3-dimensional theories is trivial. Ooguri [1] proposed recently a method for obtaining 4-manifold invariants and studying quantum gra...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1991
ISSN: 0022-4049
DOI: 10.1016/0022-4049(91)90062-7