"Naïve" yet "naivety"?

I am used to spelling "naïve" thus - "naïve". I am also used to Microsoft Word automatically changing "naive" to "naïve". Hence, I was surprised when it didn't change "naivety" to "naïvety". I then decided to work around this by letting it correct "naive" to "naïve" and then tacking on "-ty". Word then underlined "naïvety" in red and suggested a correction to "naivety".

Whether this is a typical case of "it's just a quirk of spellcheck" I am not sure, hence my question.

So:

Is it incorrect to write "naïvety"?

Alternatively:

Why is "naïvety" incorrect when "naïve" is correct?

Solution 1:

The difference could arise because naïve is a direct loan word from French, but naivety is an English word adapted from the original French naïveté.

Solution 2:

There isn’t really any standard for the use of the trema in English, so I don’t think there is any deep “why” to the behavior of this spell-checker. As mentioned in the comments, “naivety” has an anglicized spelling of the suffix, so it’s not the same as the French spelling even if you use ï. In contrast, the form naïve does exist, ï and all, in French—although unlike in English, it’s only used as the feminine form of the word. (The French masculine form naïf can sometimes be seen in English texts as a noun, but I don’t think it’s ever used in English as an adjective.)