Serializable Isolation Level

Hi all,

I am getting an exception in my code which I did not anticipate and could
not find sufficient documentation to clear this issue. I have a rather
simple table (Table_A) with two columns (Text id, Integer number). If I do
the following set of commands on two separate psql consoles, I get a
read/write exception.

T1: begin transaction isolation level serializable;
T2: begin transaction isolation level serializable;
T1: update Table_A set number = 1 where id = 'ID1';
T2: update Table_A set number = 1 where id = 'ID2';
T1: commit;
T2: commit;

T2 throws a 40001 exception. Note that both transactions operate on
distinct rows in my table. Then why am I getting an exception? I would
greatly appreciate any pointers.

Thanks,
Fran.