В отделе кадров уже получили моё заявление.

Because в отделе кадров means in the HR department, describing a location.

After в, Russian can use:

• prepositional case for location: в отделе = in the department
• accusative case for motion into somewhere: в отдел = into the department

So:

• В отделе кадров уже получили моё заявление = They have already received my application in the HR department
• Я пошёл в отдел кадров = I went to the HR department

Here the sentence is about where the receiving happened, not movement, so отделе is correct.

Кадров is the genitive plural of кадры.

The expression отдел кадров is a fixed phrase meaning personnel department / HR department. Literally, it is something like department of personnel records/staff.

So:

• отдел = department
• кадров = of personnel / of staff records

This kind of noun + genitive structure is very common in Russian:

• дом брата = brother’s house / house of the brother
• центр города = city center / center of the city
• отдел кадров = HR department / department of personnel

When the whole phrase goes into the prepositional after в, only отдел changes:

• в отделе кадров

The second noun stays genitive because it still depends on отдел.

This is a very common Russian pattern called an indefinite-personal sentence.

Russian often uses 3rd person plural with no subject when the specific people are unknown, unimportant, or obvious from context.

So получили literally means received with an understood they, but in English it is often translated more naturally as:

• They have already received my application
• My application has already been received
• The HR department has already received my application

The idea is not that some specific they has been named. It just means someone there / the relevant people did it.

This is very natural in Russian.

Because Russian often omits subjects when they are not needed.

Adding они would usually sound unnecessary here unless you want contrast or emphasis. For example:

• Они уже получили моё заявление, а вы нет = They have already received my application, but you haven’t

Without that kind of emphasis, Russian prefers just:

• уже получили

So the sentence sounds more natural without они.

It is in the accusative case, because it is the direct object of получили.

The verb получить means to receive, and the thing received goes in the accusative.

• получили что? → моё заявление

Now, заявление is a neuter inanimate noun, and for many neuter inanimate nouns, the accusative looks exactly the same as the nominative.

So:

• nominative: моё заявление
• accusative: моё заявление

They look identical, but the function in the sentence is accusative.

Because заявление is a neuter noun.

Russian adjectives and possessives must agree with the noun in gender, number, and case.

Forms of my in the nominative/accusative singular:

• мой for masculine
• моя for feminine
• моё for neuter

Since заявление is neuter, you need:

• моё заявление

Compare:

• мой паспорт = my passport
• моя анкета = my form
• моё заявление = my application / statement

Уже means already, and its position here is the most natural neutral placement.

• уже получили = have already received

Russian word order is flexible, but different positions can shift emphasis slightly.

For example:

• В отделе кадров уже получили моё заявление
  Neutral: in HR, they have already received my application.

• Моё заявление уже получили в отделе кадров
  More focus on my application.

• Уже в отделе кадров получили моё заявление
  Possible in context, but less neutral and more marked.

So the original sentence uses a very natural standard word order.

Because получили is perfective, and it presents the action as completed.

• получить = perfective, to receive as a completed event
• получать = imperfective, to be receiving / to receive repeatedly / to receive in process

In this sentence, the idea is that the application has already been received, so a completed result matters. That is why получили is the natural choice.

Compare:

• уже получили = have already received
• получали could mean were receiving / used to receive / received repeatedly, depending on context

So уже plus a completed event strongly favors получили.

It can function like either one, depending on how you translate it into natural English.

Literally, the Russian structure is closer to:

• They already received my application in HR

But because the subject is indefinite and unimportant, English often translates it more naturally as:

• My application has already been received by HR
• The HR department has already received my application

So grammatically the Russian is active, but in meaning it can feel close to an English passive.

Yes, but it does not mean exactly the same thing.

• получили заявление = received the application
• приняли заявление = accepted the application / took it in

Получили focuses on the fact that it arrived or was received.

Приняли can suggest that the office officially took it, accepted it, or processed it at the intake stage.

So both can work in some situations, but they are not always interchangeable.

Not always.

Заявление is a broad Russian word that can mean:

• application
• statement
• written request
• formal declaration

The exact English translation depends on context.

For example:

• заявление на работу = job application
• заявление в полицию = statement/report to the police
• подать заявление = submit an application / file a statement

So in your sentence, application may be correct, but in another context statement or request could be better.

A learner will often want to notice these stress patterns:

• в отделе → ат-ДЕ-ле
• кадров → КА-дров
• уже → у-ЖЕ
• получили → па-лу-ЧИ-ли
• моё → ма-ЙО
• заявление → за-яв-ЛЕ-ни-е

One especially useful point: моё is pronounced with a clear stress on the second syllable, and заявление has the stress on -ле-.

Stress is important in Russian because it can affect vowel reduction and overall natural pronunciation.