Hopf theory MOC

Biïdeal

Let B be a K-bimonoid. A biïdeal 𝐼 ≤B is at once a (two-sided) ideal and coïdeal.

• The kernel of a K-bimonoid morphism is a biïdeal.
• Given a biïdeal 𝐼 one may construct a quotient K-bimonoid B/𝐼, giving the converse of the above.

See also

• If B is a Hopf algebra, there are cases where biïdeal coïncides with Hopf ideal.

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