TJ_Q8, I'm doing this lesson again as revision. I reread your excellent contribution above, but may I suggest you edit the erroneous Russian, because it could confuse beginners in Russian, as the rest of your message is so authoritative. I would then delete my correction.
I will neglect here the English mistake that they made here, as it should be "Arabic" and not "Arab".
Anyway, your sentence, her Arabic name is a descriptive sentence; meaning there is no predicate, or in other words you are not telling someone some information (in English terms, there is no "to be" verb). And that in Arabic would be translated as اسمها العربي.
A bit of grammar, which I hope it goes smooth here:
In Arabic, and specifically in Nominal sentences (that is sentences starting with a noun and could probably have NO verbs), the subject of such sentences is typically most of the time defined (meaning it has AL to the noun). The predicate, or the information you are trying to tell (which in simple terms mostly becomes an adjective) comes without AL, i.e. indefinite.
Now, in English terms, to make sentences you would need to use the verb (to be), and thus such sentences would be: her name IS Arabic. You are telling someone, some info, about the name of some female (her). Right? Arabic in this instance (and also in Russian if you are familiar with it) do not use the verb (to be) to make such sentences. In Russian it might be (Её зовут - арабский), and the same in Arabic: اسمها عربي (literally: her-name Arabic).
The play here on telling what is the meaning of the Arabic sentence and how to translate it into English lies in noticing the definite article (AL): Does it appear with the predicate, or it doesn't? If it appears, then the word (or the adjective) in use here cannot be a predicate because a predicate must be indefinite. In other words, it would be an adjective that describes the noun attached to it; and hence in English such sentences would not be translated using the verb (to be). A Quick comparison:
- Her name is Arabic: اسمها عربي (ismuhá 3arabiy).
- Her Arabic name: اسمها العربي (ismuhá al-3arabiy).
Now, the second bit of the grammar. If you didn't know this already, adjectives do follow the noun in Arabic in general (much like Romance languages for example). However, adjectives also follow the noun they describe and attach to in terms of gender, number, and definition. Thus, if we see an adjective that follows the noun it describes by gender and number but NOT in definition, then we know that this adjective is NOT descriptive (or attributive as some language books call it). It must be predicate, and the English translation for that would include the verb (to be) or (is) in translation.
You might ask, how come اسمها (ismuhá: her name) is definite (and it must be definite because this is a nominal sentence) without having (AL) attached to it. Well, the simple answer is: the noun اسم (name) is defined by virtue of attaching a possessive article ـها (her) to it. Thus, the noun naturally becomes defined logically. Like in English, you cannot say (the her name) of course, same thing in Arabic, the noun is defined logically by adding possessive articles to it.
It's kind of long but I hope you get the idea about how important it is to notice the definite article (AL) in adjectives to define their position.