hereditary

adj

1. Passed on as an inheritance, by last will or intestate.
2. Of a title, honor or right: legally granted to somebody's descendant after that person's death.

   “Duke is a hereditary title which was created in Norman times.”

3. Of a person: holding a legally hereditary title or rank.

   “hereditary rulers”

4. Of a disease or trait: passed from a parent to offspring in the genes.

   “Haemophilia is hereditary in his family.”

   “Xanthuria is an hereditary disorder in which there is an absence of the enzyme xanthine oxidase which interferes with the metabolic breakdown of purines, leading to an increased excretion of xanthine in the urine and to formation of stones.”

5. Of a ring: such that all submodules of projective modules over the ring are also projective.
6. Of a property of graphs: such that if G has the property, so must every induced subgraph of G.

noun

1. A hereditary ruler; a hereditary peer in the House of Lords.