Fully Coprime Comodules and Fully Coprime Corings
نویسندگان
چکیده
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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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 relatio...
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Many observations about coalgebras were inspired by comparable situations for algebras. Despite the prominent role of prime algebras, the theory of a corresponding notion for coalgebras was not well understood so far. Coalgebras C over fields may be called coprime provided the dual algebra C∗ is prime. This definition, however, is not intrinsic it strongly depends on the base ring being a field...
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It is shown that the categories of R-coalgebras for a commutative unital ring R and the category of A-corings for some R-algebra A as well as their respective categories of comodules are locally presentable.
متن کاملA Zariski Topology for Bicomodules and Corings
In this paper we introduce and investigate top (bi)comodules of corings, that can be considered as dual to top (bi)modules of rings. The fully coprime spectra of such (bi)comodules attains a Zariski topology, defined in a way dual to that of defining the Zariski topology on the prime spectra of (commutative) rings. We restrict our attention in this paper to duo (bi)comodules (satisfying suitabl...
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ژورنال
عنوان ژورنال: Applied Categorical Structures
سال: 2006
ISSN: 0927-2852,1572-9095
DOI: 10.1007/s10485-006-9040-9