Using an Alias in a WHERE clause

This is not possible directly, because chronologically, WHERE happens before SELECT, which always is the last step in the execution chain.

You can do a sub-select and filter on it:

SELECT * FROM
(
  SELECT A.identifier
    , A.name
    , TO_NUMBER(DECODE( A.month_no
      , 1, 200803 
      , 2, 200804 
      , 3, 200805 
      , 4, 200806 
      , 5, 200807 
      , 6, 200808 
      , 7, 200809 
      , 8, 200810 
      , 9, 200811 
      , 10, 200812 
      , 11, 200701 
      , 12, 200702
      , NULL)) as MONTH_NO
    , TO_NUMBER(TO_CHAR(B.last_update_date, 'YYYYMM')) as UPD_DATE
  FROM table_a A
    , table_b B
  WHERE A.identifier = B.identifier
) AS inner_table
WHERE 
  MONTH_NO > UPD_DATE

Interesting bit of info moved up from the comments:

There should be no performance hit.
Oracle does not need to materialize
inner queries before applying outer
conditions — Oracle will consider
transforming this query internally and
push the predicate down into the inner
query and will do so if it is cost
effective. – Justin Cave

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