Hrushovski's finite-basis conjecture for radical well-mixed difference ideals

Let $K$ be a difference field and let $R$ be a finitely difference generated difference algebra over $K$. A difference ideal in $R$ is radical well-mixed if it is both radical and well-mixed. Hrushovski's finite-basis conjecture. Every strictly ascending chain of radical well-mixed difference ideals in $R$ is finite. This is equivalent to the assertion that every radical well-mixed difference ideal in $R$ is finitely generated. The paper proves this in the binomial case, resolving the corresponding open problem raised by E. Hrushovski.