How do I join the first row of a subquery?

This works for me:

select ir.[Invoice Number], c.[Carrier Name]
from 
    (select ROW_NUMBER() over (order by i.[Invoice Number] asc) AS RowNumber, i.[Invoice Number], i.InvoiceKey
    from Invoice i) AS ir
left join Carriers c
on ir.InvoiceKey = c.InvoiceKey
where RowNumber = 1
union all
select ir.[Invoice Number], NULL as [Carrier Name]
from 
    (select ROW_NUMBER() over (order by i.[Invoice Number] asc) AS RowNumber, i.[Invoice Number]
    from Invoice i) AS ir
where RowNumber > 1

or

select TOP 1 i.[Invoice Number], c.[Carrier Name]
from Invoice i
left join Carriers c
on i.InvoiceKey = c.InvoiceKey
union all
select ir.[Invoice Number], NULL as [Carrier Name]
from 
    (select ROW_NUMBER() over (order by i.[Invoice Number] asc) AS RowNumber, i.[Invoice Number]
    from Invoice i) AS ir
where RowNumber > 1

;with cteRowNumber as (
    select c.InvoiceKey, c.[Carrier Name], ROW_NUMBER() over (partition by c.InvoiceKey order by c.[Carrier Name]) as RowNum
        from Carriers c
)
select i.[Invoice Number],
       rn.[Carrier Name]
    from Invoice i
        left join cteRowNumber rn
            on i.InvoiceKey = rn.InvoiceKey
                and rn.RowNum = 1

This is how I would do it, using a slightly different syntax than yours (MySQL style), but I guess you could apply it to your solution as well:

SELECT i.invoiceNumber, c.carrierName
FROM Invoice as i
LEFT JOIN Carriers as c ON (c.id = (SELECT id FROM Carriers WHERE invoiceKey = i.invoiceKey ORDER BY id LIMIT 1))

This will take all records from Invoice, and join it with one (or zero) record from Carriers, specifically the record which has the same invoiceKey and only the first one.

As long as you have an index on Carriers.invoiceKey the performance of this query should be acceptable.

Sebastian

Provided that Carriers has a PRIMARY KEY called id:

SELECT  i.[Invoice Number],
        c.[Carrier Name]
FROM    Invoice i
JOIN    Carriers c
ON      c.id = 
        (
        SELECT  TOP 1 ID
        FROM    Carriers ci
        WHERE   ci.InvoiceKey = i.InvoiceKey
        ORDER BY
                id -- or whatever
        )