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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Supported by King Fahd University of Petroleum and Minerals, Research Project # INT/296.
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Abuhlail, J.Y. Fully Coprime Comodules and Fully Coprime Corings. Appl Categor Struct 14, 379–409 (2006). https://doi.org/10.1007/s10485-006-9040-9
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DOI: https://doi.org/10.1007/s10485-006-9040-9
Key words
- fully coprime (fully cosemiprime) corings
- fully coprime (fully cosemiprime) comodules
- fully coprime spectrum
- fully coprime coradical