In the article, a Nichols algebra is defined as follows. Let ${\displaystyle V\in {}_{H}^{H}{\mathcal {YD}}}$. There exists a largest ideal ${\displaystyle {\mathfrak {I}}\subset TV} $ with the following properties: \begin{align} & {\displaystyle {\mathfrak {I}}\subset \bigoplus _{n=2}^{\infty }T^{n}V,} \\ & {\displaystyle \Delta ({\mathfrak {I}})\subset {\mathfrak {I}}\otimes TV+TV\otimes {\mathfrak {I}}} \quad (\text{this is automatic}) \end{align} The Nichols algebra is \begin{align} {\displaystyle {\mathfrak {B}}(V):=TV/{\mathfrak {I}}}. \end{align} Why in the definition of a Nichols algebra we require that $V$ is a Yetter-Drinfeld module? If we take $V$ to be any vector space and define $\mathfrak{B}(V)$ using the same formulas as above, is $\mathfrak{B}(V)$ also some interesting algebra (or coalgebra)? Thank you very much.