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A Zariski Topology for Bicomodules and Corings Jawad Y. Abuhlail
 

Summary: A Zariski Topology for Bicomodules and Corings
Jawad Y. Abuhlail
Department of Mathematical Sciences, Box # 5046
King Fahd University of Petroleum & Minerals
31261 Dhahran - Saudi Arabia
abuhlail@kfupm.edu.sa
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.
1 Introduction
Several papers considered the so called top modules, i.e. modules (over commutative
rings) whose spectrum of prime submodules attains a Zariski topology, e.g. [Lu1999],
[MMS1997], [Zha1999]. Dually, we introduce and investigate top (bi)comodules for corings

  

Source: Abuhlail, Jawad Younes - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals

 

Collections: Mathematics