mysql> use test;
Database changed
mysql> CREATE TABLE shop (
-> article INT(4) UNSIGNED ZEROFILL DEFAULT '0000' NOT NULL,
-> dealer CHAR(20) DEFAULT '' NOT NULL,
-> price DOUBLE(16,2) DEFAULT '0.00' NOT NULL,
-> PRIMARY KEY(article, dealer));
Query OK, 0 rows affected (0.13 sec)

mysql> INSERT INTO shop VALUES
-> (1,'A',3.45),(1,'B',3.99),(2,'A',10.99),(3,'B',1.45),
-> (3,'C',1.69),(3,'D',1.25),(4,'D',19.95);
Query OK, 7 rows affected (0.03 sec)
Records: 7 Duplicates: 0 Warnings: 0

mysql> select * from shop;
+---------+--------+-------+
| article | dealer | price |
+---------+--------+-------+
| 0001 | A | 3.45 |
| 0001 | B | 3.99 |
| 0002 | A | 10.99 |
| 0003 | B | 1.45 |
| 0003 | C | 1.69 |
| 0003 | D | 1.25 |
| 0004 | D | 19.95 |
+---------+--------+-------+
7 rows in set (0.06 sec)

mysql> select article,max(price) from shop group by article
-> ;
+---------+------------+
| article | max(price) |
+---------+------------+
| 0001 | 3.99 |
| 0002 | 10.99 |
| 0003 | 1.69 |
| 0004 | 19.95 |
+---------+------------+
4 rows in set (0.05 sec)

mysql> select article,max(price),dealer from shop group by article;
+---------+------------+--------+
| article | max(price) | dealer |
+---------+------------+--------+
| 0001 | 3.99 | A |
| 0002 | 10.99 | A |
| 0003 | 1.69 | B |
| 0004 | 19.95 | D |
+---------+------------+--------+
4 rows in set (0.00 sec)

mysql> select article,dealer,price from shop s1
-> where price=(select max(s2.price) from shop s2
-> where s1.article=s2.article);
+---------+--------+-------+
| article | dealer | price |
+---------+--------+-------+
| 0001 | B | 3.99 |
| 0002 | A | 10.99 |
| 0003 | C | 1.69 |
| 0004 | D | 19.95 |
+---------+--------+-------+
4 rows in set (0.01 sec)

mysql> select s1.article,dealer,s1.price
-> from shop s1
-> join(
-> select article,max(price) as price from shop
-> group by article) as s2
-> on s1.article = s2.article and s1.price = s2.price;
+---------+--------+-------+
| article | dealer | price |
+---------+--------+-------+
| 0001 | B | 3.99 |
| 0002 | A | 10.99 |
| 0003 | C | 1.69 |
| 0004 | D | 19.95 |
+---------+--------+-------+
4 rows in set (0.05 sec)

mysql> select s1.article,s1.dealer,s1.price from shop s1
-> left join shop s2 on s1.article=s2.article and s1.price select s1.article,s1.dealer,s1.price,s2.* from shop s1 left join shop s2
on s1.article=s2.article and s1.price