A Zariski topology for bicomodules and corings. (English) Zbl 1182.16025

Abuhlail, Jawad Y.

Appl. Categ. Struct. 16, No. 1-2, 13-28 (2008).

This paper is a continuation of the study of fully coprime comodules. The author in this paper introduces and investigates top (bi)comodules of corings, which can be regarded as dual to top (bi)modules of rings. First, the author defines the fully coprime spectra of such (bi)comodules in a way dual to the definition of the Zariski topology on the prime spectra of (commutative) rings, and studies the interplay between the coalgebraic properties of such (bi)comodules and the introduced Zariski topology. Then, some applications and examples are given. The main application is to non-zero corings which turn out to be duo bicomodules in a canonical way. It is worth mentioning that several properties of the Zariski topology for bicomodules and corings are dual to those of the classical Zariski topolgy on the prime spectrum of commutative rings.

Reviewer: Zhang Liangyun (Nanjing)

MSC:

16T15	Coalgebras and comodules; corings
16N60	Prime and semiprime associative rings
16W80	Topological and ordered rings and modules
16D25	Ideals in associative algebras

Keywords:

fully coprime corings; fully coprime comodules; fully coprime coradicals; simple corings; simple comodules; categories of comodules; fully invariant comodules; fully coprime bicomodules; fully cosemiprime bicomodules; fully cosemiprime corings; fully coprime spectra; Zariski topologies; top bicomodules

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