"رُزّ عُمَر بارِد."

Translation: Omar's rice is cold.

[.BlueBooks.]

Shouldn't it be الرز?

[Away54]

Here رز and عمر have the structure of possession ("2al-2iDaafa" or the "muDaaf wa muDaaf 2ilaih" relationship) so رز can't be with ال as رز is the muDaaf -- attached to "Omar". This relation means that "Omar owns rice". Even though there is no ال, the "rice" itself become "definitive" indirectly because of "Omar".

[Away54]

أرزُّ عمرَ باردٌ. or رزُّ عمرَ باردٌ.