Hereditary meaning : 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. Of a person: holding a legally hereditary title or rank. Of a disease or trait: passed from a parent to offspring in the genes Of a ring: such that all submodules of projective modules over the ring are also projective.