Some remarks on linear structures in right distributive domains
-
Gunter Torner
Abstract
We examine properties of the right ideal structure of right distributive domains. Right distributive domains R are exactly those rings whose localizations at maximal right ideals M are right chain domains RM- On the one hand, the paper focuses on the question in which way properties of R are carried over to RMand vice versa. We examine the problem under which conditions two-sided ideals of R are again two-sided in the extension RM(Lemma 2.2). Further, we observe the relationship between completely prime resp. semiprime ideals of R and the extended ideals in RM. On the other hand, we prove in particular that for any maximal right ideal M = R\SMthe right-SM-saturation of a completely semiprime ideal I M of R is completely prime (Theorem 2.9). A central role is played by waists of right distributive rings which are right ideals comparable to each other ideal, in particular there exists a largest waist W which is completely prime. We present a representation theorem in terms of ideals in RW. We apply these results to the Jacobson radical J(R) of a right distributive domain R. Illustrative examples are given.
© 2025 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill-Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Contents
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill - Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Instructions to Authors
- Editors
Articles in the same Issue
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill-Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Contents
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill - Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Instructions to Authors
- Editors
