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Reading LLPSI, in PENSVM B of Capitula 2, there is this passage:

Syra ancilla Aemiliae est. Aemilia domina Syrae est.

Are Aemiliae and Syrae the direct objects, thus they are conjugated that way?

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The the word ancilla and the names Syra and Aemilia are declined (rather than conjugated) according to the first declension, as shown in the following chart from Allen and Greenough's Latin Grammar:

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The different forms of the declensions indicate the function of the nouns in a sentence. They often do the work of what we do with prepositional phrases. Rather than the prepositional phrase of the star, the same idea can be expressed in Latin with a single word: stellae.

From the chart, you can see that the -a ending indicates the nominative singular. (It could also indicate the ablative singular, but that possibility is ruled out by the context.) The nominative singular is what's to be expected for the subject and predicate of sentences of the verb sum (or esse when indicated by the infinitive):

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From the first chart, you can also see that the -ae indicates either the nominative plural, or the genitive or dative singular. The plural doesn't make sense because it's only one person, so that leaves either the genitive or the dative singular. For the given context, the genitive makes more sense, because the meaning is of Syra or of Aemillia.

From that we can conclude that the sentences mean:

Syra is the servant of Aemilia. Aemilia is the mistress of Syra.

Of course, in English, that can be stated more simply by saying:

Syra is Aemilia's servant. Aemilia is Syra's mistress.

Sentences of the verb sum don't have direct objects (except perhaps in subordinate clauses). Rather, direct object follow transitive verbs. Any noun that serves as a direct object will appear in the accusative. Here's an example:

Caesar librum amavit.

In this sentence librum is the direct object: Caesar loved the book. Because of that, librum appears in the accusative singular. Being of the second declension its ending is -um.

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