help w/ query

Anyone help w/ the following sql query ... Here's my tables ...

table A
id      name
-----|-------
1000 AA
1001  AB
1002 AC
1003 AD

table B
id  pid
-----|-------
1000 1000
1001 1000
1002 1000
1003 1001
1004 1001

Here's my query, (note that 'AA' is all the info I provide, 
cause that's the ) ...

SELECT B.id FROM B, A WHERE B.pid = A.id AND A.name = 'AA';

Returns the following resultset ...

id (note, this is from B, but all have pid's of 1000)
------
1000
1001
1002

When what I really want returned is the 1000 from B's table 
and only that record ...

id (note, this is what I want from B)
------
1000 

Any idea how to grab this?

TIA