MySQL 8.0

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create table my_table (
  field1 varchar(5),		
  field2 int
);

insert into my_table values
('AAA',1),
('AAA',2),
('AAA',0),
('BBB',1),
('BBB',2),
('CCC',0),
('CCC',2),
('DDD',3);

Records: 8  Duplicates: 0  Warnings: 0


select * from my_table;


field1
field2


AAA
1

AAA
2

AAA
0

BBB
1

BBB
2

CCC
0

CCC
2

DDD
3


select m.* 
from my_table m
where not exists (select 1 from my_table mt  where m.field1 = mt.field1 and field2 = 0);


field1
field2


BBB
1

BBB
2

DDD
3


select field1 
from my_table
group by field1
having min(field2) <> 0;


field1


BBB

DDD