# Journal of the Ramanujan Mathematical Society

Volume 38, Issue 1, March 2023 pp. 33–46.

Transversal intersection and sum of polynomial ideals

**Authors**:
Joydip Saha, Indranath Sengupta and Gaurab Tripathi

**Author institution:**
Stat-Math Unit, Indian Statistical Institute, 203 B. T. Road,
Kolkata 700 108, India.

**Summary: **
In this paper we derive some conditions for transversal intersection of
polynomial ideals and present some examples. Finally, as an application
of the results proved, we compute the Betti numbers of ideals of the form
I{1}(XY) + J, where X and Y are some generic or generic symmetric
matrices and J is the ideal generated
by the 2× 2 minors of the matrix consisting of any two rows of X.

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