A Zariski Topology for Bicomodules and Corings

Details A Zariski Topology for Bicomodules and Corings A Zariski Topology for Bicomodules and Corings

2006-12-31

arxiv.org/abs/math/0701025v2

Mathematics

Rings and Algebras

(SUBMITTED). Several misprints in the 1st version have been corrected

Scientific paper

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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