On Coprime Modules and Comodules

@article{Wijayanti2009OnCM,
  title={On Coprime Modules and Comodules},
  author={Indah Emilia Wijayanti and Robert Wisbauer},
  journal={Communications in Algebra},
  year={2009},
  volume={37},
  pages={1308 - 1333}
}
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. The purpose of the article is to provide a better understanding of related notions for coalgebras… 
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References

SHOWING 1-10 OF 39 REFERENCES
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
ON PRIME AND SEMIPRIME MODULES AND COMODULES
In this paper we describe the structure of prime and semiprime R-modules M such that R/AnnR(M) is artinian. The obtained results are then applied to describe the structure of prime and semiprime
Torsion theories for coalgebras
Primeness described in the language of torsion preradicals
The objects of study in this paper are lattice ordered monoids. These are structures 〈L;⊕, 0L; ≤〉 where 〈L⊕, 0L〉 is a monoid, 〈L;≤〉 is a lattice and the binary operation ⊕ distributes over finite
Properly semiprime self-pp-modules
In an earlier paper [8] the authors introduced strongly and properly semiprime modules. Here properly semiprime modules M are investigated under the condition that every cyclic submodule is
Colocalization on Grothendieck Categories with Applications to Coalgebras
Rings and modules of quotients with respect to an additive topology F or a localizing subcategory of R y Mod were introduced by Gabriel in his w x thesis 3 , and have been an important tool in ring
Coprime preradicals and modules
The Torsion Theory Cogenerated by M-Small Modules
Abstract Let M and N be R-modules. We define where S denotes the class of all M-small modules. We call N an M-cosingular (non-M-cosingular) module if Z M (N) = 0 ( Z M (N) = N). We study the
Duprime and dusemiprime modules
PRIME PATH COALGEBRAS
We develop the notion of primeness in coalgebras (over a commutative field). In particular, in this work we focus our attention on the study and characterization of prime subcoalgebras of path
...
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