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));

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);

SELECT s1.*
FROM shop s1
LEFT JOIN shop s2 ON s1.article = s2.article AND s1.price < s2.price
WHERE s2.price IS NULL;

+---------+--------+-------+
| 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 |
+---------+--------+-------+

SELECT *
FROM shop s1
LEFT JOIN shop s2 ON s1.article = s2.article AND s1.price < s2.price;

+---------+--------+-------+---------+--------+-------+
| article | dealer | price | article | dealer | price |
+---------+--------+-------+---------+--------+-------+
|    0001 | A      |  3.45 |    0001 | B      |  3.99 |
|    0001 | B      |  3.99 |    NULL | NULL   |  NULL |
|    0002 | A      | 10.99 |    NULL | NULL   |  NULL |
|    0003 | B      |  1.45 |    0003 | C      |  1.69 |
|    0003 | C      |  1.69 |    NULL | NULL   |  NULL |
|    0003 | D      |  1.25 |    0003 | B      |  1.45 |
|    0003 | D      |  1.25 |    0003 | C      |  1.69 |
|    0004 | D      | 19.95 |    NULL | NULL   |  NULL |
+---------+--------+-------+---------+--------+-------+

SELECT *
FROM shop s1
LEFT JOIN shop s2 ON s1.article = s2.article;

+---------+--------+-------+---------+--------+-------+
| article | dealer | price | article | dealer | price |
+---------+--------+-------+---------+--------+-------+
|    0001 | A      |  3.45 |    0001 | A      |  3.45 |
|    0001 | A      |  3.45 |    0001 | B      |  3.99 |
|    0001 | B      |  3.99 |    0001 | A      |  3.45 |
|    0001 | B      |  3.99 |    0001 | B      |  3.99 |
|    0002 | A      | 10.99 |    0002 | A      | 10.99 |
|    0003 | B      |  1.45 |    0003 | B      |  1.45 |
|    0003 | B      |  1.45 |    0003 | C      |  1.69 |
|    0003 | B      |  1.45 |    0003 | D      |  1.25 |
|    0003 | C      |  1.69 |    0003 | B      |  1.45 |
|    0003 | C      |  1.69 |    0003 | C      |  1.69 |
|    0003 | C      |  1.69 |    0003 | D      |  1.25 |
|    0003 | D      |  1.25 |    0003 | B      |  1.45 |
|    0003 | D      |  1.25 |    0003 | C      |  1.69 |
|    0003 | D      |  1.25 |    0003 | D      |  1.25 |
|    0004 | D      | 19.95 |    0004 | D      | 19.95 |
+---------+--------+-------+---------+--------+-------+

`|    0001 | A      |  3.45 |    0001 | A      |  3.45 |`

`|    0001 | B      |  3.99 |    0001 | A      |  3.45 |`