Fully Coprime Comodules and Fully Coprime Corings

Details Fully Coprime Comodules and Fully Coprime Corings Fully Coprime Comodules and Fully Coprime Corings

2006-04-12

arxiv.org/abs/math/0604285v2

Applied Categorical Structures (Special Issue 2006)

Mathematics

Rings and Algebras

31 Pages

Scientific paper

Prime objects were defined as generalization of simple objects in the categories of rings (modules). In this paper we introduce and investigate what turns out to be a suitable generalization of simple corings (simple comodules), namely fully coprime corings (fully coprime comodules). Moreover, we consider several primeness notions in the category of comodules of a given coring and investigate their relations with the fully coprimeness and the simplicity of these comodules. These notions are applied then to study primeness and coprimeness properties of a given coring, considered as an object in its category of right (left) comodules.

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