caa a22 4500 467882622 CHVBK 20180406152724.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s10485-006-9040-9 doi (NATIONALLICENCE)springer-10.1007/s10485-006-9040-9 Abuhlail Jawad Department of Mathematical Sciences, Box # 5046, King Fahd University of Petroleum and Minerals, 31261, Dhahran, Saudi Arabia aut Fully Coprime Comodules and Fully Coprime Corings [Elektronische Daten] [Jawad Abuhlail] 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. Springer Science + Business Media B.V., 2006 fully coprime (fully cosemiprime) corings nationallicence fully coprime (fully cosemiprime) comodules nationallicence fully coprime spectrum nationallicence fully coprime coradical nationallicence Applied Categorical Structures Kluwer Academic Publishers 14/5-6(2006-12-01), 379-409 0927-2852 14:5-6<379 2006 14 10485 https://doi.org/10.1007/s10485-006-9040-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-006-9040-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Abuhlail Jawad Department of Mathematical Sciences, Box # 5046, King Fahd University of Petroleum and Minerals, 31261, Dhahran, Saudi Arabia aut NATIONALLICENCE 773 0- Applied Categorical Structures Kluwer Academic Publishers 14/5-6(2006-12-01), 379-409 0927-2852 14:5-6<379 2006 14 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer