The structure in the nucleus that contains hereditary material is the chromosomes.

Here's a breakdown:

* Nucleus: The control center of the cell, containing the genetic material.

* Chromosomes: Long, thread-like structures made up of DNA (deoxyribonucleic acid) and proteins. DNA holds the genetic instructions for building and maintaining an organism.

* DNA: The molecule that carries the genetic code.

* Genes: Specific segments of DNA that code for specific traits.

So, the chromosomes within the nucleus are the structures that store and transmit the hereditary information from one generation to the next.