A question of object inheritance behaviour

I have created a table , let's say "people" that has a column called
"id".
I declared this column as "serial", that means unique, sequential
assigned values.

I have created another table, "students", that inherits the columns from
"people" and has other fields, let's say "university".

The "students" table inherits the sequential attribute of it's parent
table, "people", but lacks the attribute of unique field.

I realise that a unique key index is builded and maintained at table
instance level, but this case seems to me that it's a "half-inheritance
behaviour". How do you feel about it ? From my point of view, a "unique"
attribute of a field declared at parent level should be inherited
through all instances of that table.

Constantin Teodorescu
FLEX Consulting Braila, ROMANIA