Fully Coprime Comodules and Fully Coprime Corings |
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Authors: | Jawad Y Abuhlail |
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Institution: | (1) Department of Mathematical Sciences, Box # 5046, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Saudi Arabia |
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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.
Supported by King Fahd University of Petroleum and Minerals, Research Project # INT/296. |
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Keywords: | fully coprime (fully cosemiprime) corings fully coprime (fully cosemiprime) comodules fully coprime spectrum fully coprime coradical |
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