Coprime Comodules and Coprime Corings
نویسنده
چکیده
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 coprime corings (coprime comodules). Moreover, we consider several primeness notions in the category of comodules of a given coring and investigate their relations with the coprimeness and the simplicity of these comodules. These notions are applied then to study primeness and coprimeness properties of any given coring, considered as an object in its category of right (left) comodules.
منابع مشابه
Fully Coprime Comodules and Fully Coprime Corings
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 t...
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