Just to recap, the standard solution uses an uncorrelated subquery and looks like this:
SELECT x.*
FROM my_table x
JOIN (SELECT grouping_criteria,MAX(ranking_criterion) max_n FROM my_table GROUP BY grouping_criteria) y
ON y.grouping_criteria = x.grouping_criteria
AND y.max_n = x.ranking_criterion;
If you're using an ancient version of MySQL, or a fairly small data set, then you can use the following method:
SELECT x.*
FROM my_table x
LEFT
JOIN my_table y
ON y.joining_criteria = x.joining_criteria
AND y.ranking_criteria < x.ranking_criteria
WHERE y.some_non_null_column IS NULL;