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.
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Supported by King Fahd University of Petroleum & Minerals, Research Project # INT/296.
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Abuhlail, J.Y. A Zariski Topology for Bicomodules and Corings. Appl Categor Struct 16, 13–28 (2008). https://doi.org/10.1007/s10485-007-9088-1
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DOI: https://doi.org/10.1007/s10485-007-9088-1
Keywords
- Fully coprime (bi)comodules
- Fully cosemiprime (bi)comodules
- Fully coprime corings
- Fully cosemiprime corings
- Fully coprime spectrum
- Fully coprime coradical
- Zariski topology
- Top (bi)comodules