MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If $H$ is a Hopf algebra over a field and $K$ is a right or left coideal of $H$ then $K^+=K\cap\ker\epsilon$ is a coideal of $H$. Does this hold when $k$ is a commutative ring? If not, what is a counterexample?


share|cite|improve this question
(Note: It is rather easy to prove that $\left(\eta \varepsilon - \operatorname{id}\right)\left(K\right)$ is a coideal of $H$, because every $k \in K$ satisfies $\Delta\left(k - \varepsilon\left(k\right)\right) = \sum_{(k)} \left(k_{(1)} - \varepsilon\left(k_{(1)}\right)\right) \otimes k_{(2)} + 1 \otimes \left(k - \varepsilon\left(k\right)\right)$, using Sweedler's notation.) – darij grinberg Aug 1 '14 at 12:47

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.