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Generalized coderivations of bicomodules. (English) Zbl 1346.16029

In a previous paper, [Int. J. Pure Appl. Math. 77, No. 4, 579-593 (2012; Zbl 1253.16041)], the author extended a generalized derivation to a map from a bimodule to a bimodule. By dualizing, it is possible to extend the definition of a generalized coderivation to a map from a bicomodule to a bicomodule over corings. The main goal of this paper is to investigate this new generalized coderivation. In particular, in section \(3\) the author constructs a universal generalized coderivation. He shows in section \(4\) that, for each \((\mathcal{D,C})\)-bicomodule \(N\) over corings \(\mathcal C\) and \(\mathcal D\), there exists a \((\mathcal{D,C})\)-bicomodule \(\mathcal U(N)\) that is isomorphic to the cotensor product of \(N\) and \(\mathcal U(\mathcal D\otimes_R\mathcal C)\). The paper finishes giving in section \(5\) a characterization of a coseparable coring.

MSC:

16T15 Coalgebras and comodules; corings
16W25 Derivations, actions of Lie algebras

Citations:

Zbl 1253.16041
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References:

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