hereditary

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

Passed on as an inheritance, by last will or intestate.

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.”

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

“hereditary rulers”

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

“Haemophilia is hereditary in his family.”

Of a ring: such that all submodules of projective modules over the ring are also projective.