Mysql 无主键的SQL连接

我有两个表（A和B），它们不共享主键。我需要某种连接，对于表A中的每一行，如果date\u B，我必须添加表B行

*日期格式：yyyy-mm-dd

表A

+-------+-----+-----------+
| id_A  | op_A|   date_A  |
+-------+-----+-----------+
| 1     |  0  | 2018-10-01|
| 2     |  0  | 2018-12-31| 
+-------+-----+-----------+

表B

+-----+--------+-------------+
| id_b| other  |  date_B     |
+-----+--------+-------------+
| a   |  8     | 2018-09-01  |
| b   |  90    | 2018-12-01  | 
+-----+--------+-------------+

正确结果：

+-----+-----+-----------+-----+--------+-------------+
| id_A| op_A|   date_A  | id_B| other  |  date_B     |
+-----+-----+-----------+-----+--------+-------------+
| 1   |  0  | 2018-10-01| a   |  8     | 2018-09-01  |
| 2   |  0  | 2018-12-31| a   |  8     | 2018-09-01  |
| 2   |  0  | 2018-12-31| b   |  90    | 2018-12-01  |  
+-----+-----+-----------+-----+--------+-------------+

---

此查询应提供所需的结果：

SELECT *
FROM TableA a
JOIN TableB b ON b.date_B < a.date_A

---

完美！谢谢

id_A    op_A    date_A      id_b    other   date_B
1       0       2018-10-01  a       8       2018-09-01
2       0       2018-12-31  a       8       2018-09-01
2       0       2018-12-31  b       90      2018-12-01