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SQL query with Highest value with tie

I am trying to write a query that lists students who have earned the highest total credit in each department. I have to also include tied students in the result. The query should return relation with department name, student name and total credit they earned.

SELECT s.dept_name, s.name, s.max
FROM (SELECT dept_name, name, MAX(tot_cred) as max 
      FROM university.student GROUP BY dept_name) as s,
     university.student as t
WHERE s.name = t.name;

It is giving errors and I don't know how to deal with ties. If I delete the name part in the query, I have managed to get the highest credits in each department(without a tie)

The table student consists of an ID, name, department, total credit.

Use RANK() window function:

SELECT t.dept_name, t.name, t.tot_cred
FROM (
  SELECT dept_name, name, tot_cred, 
    RANK() OVER(PARTITION BY dept_name ORDER BY tot_cred DESC) rn
  FROM university.student 
) t
WHERE t.rn = 1

This is an alternative in case you can't use window functions:

SELECT s.dept_name, s.name, s.tot_cred
FROM university.student s
INNER JOIN (
  SELECT dept_name, MAX(tot_cred) tot_cred
  FROM university.student
  GROUP BY dept_name
) t ON t.dept_name = s.dept_name AND s.tot_cred = t.tot_cred

or with NOT EXISTS :

SELECT s.dept_name, s.name, s.tot_cred 
FROM university.student s 
WHERE NOT EXISTS (
  SELECT 1 FROM university.student
  WHERE dept_name = s.dept_name AND tot_cred > s.tot_cred  
)

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