Open Access
January, 2016 Generalized coderivations of bicomodules
J. Math. Soc. Japan 68(1): 425-440 (January, 2016). DOI: 10.2969/jmsj/06810425


We introduce a generalized coderivation from a bicomodule to a bicomodule over corings, which is a generalization of a coderivation. For each $({\mathcal D},{\mathcal C})$-bicomodule $N$ over corings ${\mathcal C}$ and ${\mathcal D}$, we construct the universal generalized coderivation $\upsilon_N:{\mathcal U}(N)\to N$ such that every generalized coderivation from a $({\mathcal D},{\mathcal C})$-bicomodule $M$ to $N$ is uniquely expressed as $\upsilon_N\circ f$ with some $({\mathcal D},{\mathcal C})$-bicomodule map $f:M\to{\mathcal U}(N)$. ${\mathcal U}(N)$ is isomorphic to the cotensor product of $N$ and ${\mathcal U}({\mathcal D}\otimes_R{\mathcal C})$. We show that a coring ${\mathcal C}$ is coseparable if and only if, for any coring ${\mathcal D}$, all generalized coderivations from a $({\mathcal D},{\mathcal C})$-bicomodule to a $({\mathcal D},{\mathcal C})$-bicomodule are inner.


Download Citation

Hiroaki KOMATSU. "Generalized coderivations of bicomodules." J. Math. Soc. Japan 68 (1) 425 - 440, January, 2016.


Published: January, 2016
First available in Project Euclid: 25 January 2016

zbMATH: 1346.16029
MathSciNet: MR3454565
Digital Object Identifier: 10.2969/jmsj/06810425

Primary: 16T15

Keywords: coring , coseparable coring , generalized coderivation

Rights: Copyright © 2016 Mathematical Society of Japan

Vol.68 • No. 1 • January, 2016
Back to Top