我需要修改一个已经存在的表。起始表如下：

create TABLE schema.students(
  id_students int(11) NOT NULL AUTO_INCREMENT,
  data_signUP date NOT NULL,
  description varchar(100) CHARACTER SET latin1 COLLATE latin1_bin NOT NULL,
  id_university int(11) NOT NULL,
  PRIMARY KEY (id_students),
  KEY id_university(id_university),
  CONSTRAINT students_university_FK FOREIGN KEY (id_university) REFERENCES university(id_university)
) ENGINE=InnoDB AUTO_INCREMENT=1 DEFAULT CHARSET=latin1 COLLATE=latin1_general_ci;

现在我需要修改表并在表exams（id\u exams）中添加另一个fk，我还需要修改列“description”，该列最初不为null，但现在可以为null，因此我要：

alter TABLE schema.students(
      id_students int(11) NOT NULL AUTO_INCREMENT,
      data_signUP date NOT NULL,
      add description varchar(100) CHARACTER SET latin1 COLLATE latin1_bin DEFAULT NULL,
      id_university int(11) NOT NULL,
 id_exam int(11) NOT NULL,
      PRIMARY KEY (id_students),
      KEY id_university(id_university),
 ADD KEY id_exam(id_exam),
      CONSTRAINT students_university_FK FOREIGN KEY (id_university) REFERENCES university(id_university),
CONSTRAINT students_exams_FK FOREIGN KEY (id_exam) REFERENCES exams(id_exam)
    ) ENGINE=InnoDB AUTO_INCREMENT=1 DEFAULT CHARSET=latin1 COLLATE=latin1_general_ci;

有人能帮我吗？