Does trigger has a schema? (Microsoft SQL Server)

I was wondering if triggers have (or belongs to) schemas.

According to MSDN syntax for CREATE TRIGGER is:

CREATE TRIGGER [ schema_name . ]trigger_name 
ON { table | view } 
[ WITH <dml_trigger_option> [ ,...n ] ]
{ FOR | AFTER | INSTEAD OF } 
{ [ INSERT ] [ , ] [ UPDATE ] [ , ] [ DELETE ] } 
[ NOT FOR REPLICATION ] 
AS { sql_statement  [ ; ] [ ,...n ] | EXTERNAL NAME <method specifier [ ; ] > }

But when you expand triggers node under table node in SQL Server Management Studio (SSMS) trigger schema is not shown. Also if you query sys.triggers view there is no schema_id column. But when you query for your trigger name sys.objects views there IS schema_id column. So where is the truth?

So in my lab I made a simple test. I tried to add to one table two triggers with the same name but different schemas, and it occures that:

Msg 2103, Level 15, State 1, Procedure MyNewTrigger, Line 14 Cannot create trigger 'schema2.MyNewTrigger' because its schema is different from the schema of the target table or view.

Conclusion: Trigger has a schema but it has to be the same schema as schema of the table. So it's some way safe to avoid giving schema names together with trigger name in scripts.