Abstract
In this paper we introduce and investigate top (bi)comodules of corings, that can be considered as dual to top (bi)modules of rings. The fully coprime spectra of such (bi)comodules attains a Zariski topology, defined in a way dual to that of defining the Zariski topology on the prime spectra of (commutative) rings. We restrict our attention in this paper to duo (bi)comodules (satisfying suitable conditions) and study the interplay between the coalgebraic properties of such (bi)comodules and the introduced Zariski topology. In particular, we apply our results to introduce a Zariski topology on the fully coprime spectrum of a given non-zero coring considered canonically as duo object in its category of bicomodules.
| Original language | English |
|---|---|
| Pages (from-to) | 13-28 |
| Number of pages | 16 |
| Journal | Applied Categorical Structures |
| Volume | 16 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - Apr 2008 |
Bibliographical note
Funding Information:Acknowledgements The author is grateful for the financial support and the excellent research facilities provided by KFUPM.
Funding Information:
Supported by King Fahd University of Petroleum & Minerals, Research Project # INT/296.
Keywords
- Fully coprime (bi)comodules
- Fully coprime coradical
- Fully coprime corings
- Fully coprime spectrum
- Fully cosemiprime (bi)comodules
- Fully cosemiprime corings
- Top (bi)comodules
- Zariski topology
ASJC Scopus subject areas
- Theoretical Computer Science
- Algebra and Number Theory
- General Computer Science