Transversal Intersection and Sum of Polynomial Ideals
Abstract
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 $X$.
 Publication:

arXiv eprints
 Pub Date:
 November 2016
 arXiv:
 arXiv:1611.04732
 Bibcode:
 2016arXiv161104732S
 Keywords:

 Mathematics  Commutative Algebra;
 13D02 (Primary);
 13C40;
 13P10;
 13D07 (Secondary)