Transversal Intersection and Sum of Polynomial Ideals
  In this paper we derive some conditions for transversal intersection of polynomial ideals. We exhibit some examples. Finally, as an application of the results proved, we compute the Betti numbers for ideals of the form $I_{1}(XY) + J$, where $X$ and $Y$ are matrices and $J$ is the ideal generated by the $2\times 2$ minors of the matrix consisting of any two rows of $X$. 
Joydip Saha, Indranath Sengupta, Gaurab Tripathi
math.AC