so if we're given that L extends K, w/ L algebraic of K, and M extends L, w/ M algebraic over L, do we get that M is algebraic of K? (we may not assume finite extensions)

that is:

For all l in L, there exists p(t) in K[t] such that p(l)=0

For all m in M, there exists q(t) in L[t] such that q(m)=0

For all m in M, does there exist r(t) in K[t] such that r(m)=0?

thanks for any help