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Fully Coprime Comodules and Fully Coprime Corings

Jawad A. Abuhlail
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Abstract

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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Jawad A. Abuhlail. 2006-10-07. Fully Coprime Comodules and Fully Coprime Corings. https://arxiv.org/abs/math/0604285

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