Let $R$ be a ring and let $X_1,\dotsc,X_\ell$ be algebraically independent variables over $R$. Then we have a polynomial ring $R[X_1,\dotsc,X_\ell]$.
I asked my lecturer why we need them to be algebraically independent and he answered that "because you need to make sure that you have a polynomial ring when you adjoint these elements"
I did not fully understand what he meant by "adjoint".
what happens when they are not linearly independent? keep in mind that my English is not my first language.