Weakly minimal modules over integral group rings and over related classes of rings
β Scribed by Stefano Leonesi; Sonia L'Innocente; Carlo Toffalori
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 204 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
β¦ Synopsis
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, PrΓΌfer domains and integral group rings.
π SIMILAR VOLUMES
We introduce and impose conditions under which the finitely generated essential right ideals of E may be classified in terms of k-submodules of M. This yields a classification of the domains Morita equivalent to E when E is a Noetherian domain. For example, a special case of our results is:
I prove that given a finite semigroup or finite associative ring S and a system βΊ of equations of the form ax s b or xa s b, where a, b g S, x is an unknown, it is algorithmically impossible to decide whether or not βΊ is solvable over S, that is, Ε½ whether or not there exists a bigger semigroup or r