hosyousyo ni seizoubangou ga kaite arimasu.

Here, に marks the place where something is located or where a result exists.

So 保証書に製造番号が書いてあります means the serial number exists in a written form on the warranty card.

In this kind of sentence, に often translates as on, in, or at, depending on the natural English wording.

Pattern:

• A に B が書いてある = B is written on/in A

Because this sentence is describing a state, not the action of writing.

Compare these:

• 製造番号を書く
  = write the serial number
  Here, 製造番号 is the direct object, so it takes を.

• 製造番号が書いてある
  = the serial number is written
  Here, the serial number is the thing in the resulting state, so it takes が.

This is very common with the 〜てある pattern: the thing affected by the action shows up as the subject with が.

書いてあります is 書く in the 〜てある pattern.

Structure:

• 書く → 書いて
• 書いてある = to be in the state of having been written

This pattern means:

• someone intentionally did the action
• the result still remains

So 書いてあります does not focus on the person writing. It focuses on the fact that the writing is there now.

This is a very common question.

書いています usually focuses more on the action or activity of writing, or sometimes a more general ongoing state depending on context.

書いてあります focuses on the resulting condition: something has been written there and remains there.

In a sentence like this, where you mean information is present on a document, 書いてあります is very natural.

Very roughly:

• 書いています = is writing / writes / is written, depending on context
• 書いてあります = has been written there and is there now

No. It is not passive.

It is the 〜てある construction, which is different from the passive.

Compare:

• 製造番号が書いてあります
  = the serial number is written there / has been written there

• 製造番号が書かれています
  = the serial number is written / has been written
  This is passive.

The difference in nuance is that 〜てある often suggests an intentional action done for some purpose, with attention on the result that now exists.

Because 〜てある is a fixed grammar pattern, and it always uses ある.

Also, ある is used for inanimate things, and written text on a document is inanimate.

So in this construction, いる is not used.

Not necessarily.

In Japanese, 書く can be used quite broadly for information that appears in writing, including things that are handwritten, printed, typed, or otherwise written on a document.

So even if the serial number is printed, 書いてあります is still natural.

Because this version is just a neutral statement of fact.

Japanese often leaves out は when simply presenting information.

If you add は, the focus changes a little:

• 保証書には製造番号が書いてあります。
  = On the warranty card, the serial number is written.
  This puts more focus or contrast on the warranty card.

• 製造番号は保証書に書いてあります。
  = The serial number is written on the warranty card.
  This puts serial number in the topic position.

So the original sentence is a straightforward, neutral description.

Not completely.

The most basic rule is that the verb comes at the end. Before that, Japanese word order is fairly flexible.

So these are both possible:

• 保証書に製造番号が書いてあります。
• 製造番号が保証書に書いてあります。

They mean almost the same thing, but the emphasis can shift slightly depending on what comes first.

The plain form is 書いてある.

Breakdown:

• dictionary form: 書く
• te-form: 書いて
• plain resultative form: 書いてある
• polite form: 書いてあります

So 書いてあります is just the polite version of 書いてある.