A module M is called a CS-module if every submodule of M is essential in a direct summand of M. A ring R is called CS-semisimple if every right R-module is CS. For a ring R, we show that: Ž . 1 R is right artinian with Jacobson radical cube zero if every countably generated right R-module is a dire
Some EC∑ Classes of Rings
✍ Scribed by John T. Baldwin
- Publisher
- John Wiley and Sons
- Year
- 1978
- Tongue
- English
- Weight
- 272 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0044-3050
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📜 SIMILAR VOLUMES
We present a generalization of Gevrey classes, aiming at including the inhomogeneous Gevrey functions introduced by Liess [15] and the ultradifferentiable functions in the sense of Braun et al. [4]. Therefore, we treat the related dual spaces, called generalized Gevrey ultradistributions, proving al
A module is weakly minimal if and only if every pp-definable subgroup is either finite or of finite index. We study weakly minimal modules over several classes of rings, including valuation domains, Prüfer domains and integral group rings.
A general conjecture is given for an explicit basis of the coordinate ring of the closure of the conjugacy class of a nilpotent matrix. This conjecture is proven when the partition given by the transpose Jordan type of the nilpotent matrix is a hook or has two parts.